Academic Publications

1981



(1) M.Tsutsumi and N.Hayashi: Classical solutions of nonlinear Schrödinger equations in higher dimensions, Math. Z., 177, 217-234, 1981


1986



(2) N.Hayashi: Classical solutions of nonlinear Schrödinger equations, Manuscripta Math. 55 , 171-190,1986
(3) N.Hayashi: Global strong solutions of coupled Klein-Gordon-Schrödinger
 equations, Funkcialaj Ekvacioj,29 ,299-307,1986
(4) N.Hayashi and M.Tsutsumi: $L^\infty$-decay of classical solutions for nonlinear Schrödinger equations, Proceeding of the Royal Society of Edinburgh, 104A, 309-327,1986
(5) N.Hayashi, K.Nakamitsu and M.Tsutsumi: On solutions of the initial value problem for nonlinear Schrödinger equations in one space dimension, Math. Z., 192, 637-650,1986


1987



(6) N.Hayashi, K.Nakamitsu and M.Tsutsumi: On solutions of the initial value problem for nonlinear Schrödinger equations, J. Funct. Anal.71, 218-245,1987
(7) N.Hayashi and W. von Wahl: On the global strong solutions of coupled Klein-Gordon-Schrödinger equations, J. Math. Soc. Japan, 39, 489-499,1987
(8) N.Hayashi and Y.Tsutsumi: Scattering theory for Hartree type equations, Ann. Inst. Henri. Poincare, Physique Theorique, 46,187-213,1987
(9) N.Hayashi and T.Ozawa: Time decay of solutions to the Cauchy problem for time-dependent Schrödinger-Hartree equations, Commun. Math. Phys., 110, 467-478,1987


1988



(10) N.Hayashi: Asymptotic behavior of solutions to time-dependent Hartree equations, Nonlinear Anal. (TMA), 12,313-319,1988
(11) N.Hayashi and T.Ozawa: Scattering theory in the weighted $L^2({R}^n)$ spaces for some Schrödinger equations, Ann. Inst. Henri. Poincare, Physique Theorique, 48, 17-37, 1988
(12) N.Hayashi, K.Nakamitsu and M.Tsutsumi: Nonlinear Schrödinger equations in weighted Sobolev space, Funkcialaj Ekvacioj, 31,363-381,1988


1989



(13) N.Hayashi and T.Ozawa: Smoothing effect for some Schrödinger equations, J. Funct. Anal., 85, 307-348,1989
(14) N.Hayashi and T.Ozawa: Time decay for some Schrödinger equations, Math.Z., 200, 467-484,1989
(15) N.Hayashi Time decay of solutions to the Schrödinger equation in exterior domains. I,  Ann. Inst. Henri. Poincare, Physique Theorique, 50, 71-81,1989
(16) N.Hayashi: Time decay of solutions to the Schrödinger equation in exterior domains. II,  Ann. Inst. Henri. Poincare, Physique Theorique, 50,83-93,1989
(17) T.Ozawa and N.Hayashi: Lower bounds for order of decay or of growth in time for solutions to linear and non-linear Schrödinger equations, Publ. RIMS, Kyoto Univ., 25, 847-859,1989


1990


(18) N.Hayashi: Smoothing effect for nonlinear Schrödinger equations in exterior domains, J. Funct. Anal. 89, 444-458,1990
(19) N.Hayashi and S.Saitoh: Analyticity and smoothing effect for the Schrödinger equation, Ann. Inst. Henri. Poincare, Physique Theorique, 52, 163-173,1990
(20) N.Hayashi and S.Saitoh: Analyticity and global existence of small solutions to some nonlinear Schrödinger equations, Commun. Math. Phys., 129,27-42,1990
(21) H. Aikawa, N.Hayashi and S.Saitoh: The Bergman space on a sector and the heat equation, Complex Variables, 15, 27-36,1990
(22) N.Hayashi: Global existence of small analytic solutions to nonlinear Schödinger equations, Duke Math. J., 60, 717-727,1990


1991



(23) H. Aikawa, N.Hayashi and S.Saitoh: Isometrical identities for the Bergman and the Szegö spaces on a sector, J. Math. Soc. Japan, 43,195-201,1991
(24) H. Aikawa and N.Hayashi: Holomorphic solutions of semilinear heat equations, Complex Variables, 16, 115-125,1991
(25) H. Aikawa, N.Hayashi, I.Onda and S.Saitoh: Analytical extensions of the members of the Bergman and Szegö spaces on some tube domains, Archiv der Mathematik, 56, 362-369,1991
(26) N.Hayashi: Solutions of the (generalized) Korteweg-de Vries equationin the Bergman and the Szegö spaces on a sector, Duke Math. J., 62, 575-591, 1991
(27) N.Hayashi: Analyticity of solutions of the Korteweg-de Vries equation, SIAM J. Math. Anal, 22, 1738-1743,1991


1992


(28) N.Hayashi and T.Ozawa: On the derivative nonlinear Schrödinger equations, Physica D, 55, 14-36,1992
(29) N.Hayashi: Smoothing effect of small analytic solutions to nonlinear Schrödinger equations, Ann. Inst. Henri. Poincare, Physique Theorique, 57,385-394,1992


1993


(30) N.Hayashi: The initial value problem for the derivative nonlinear Schödinger equations in the energy space, Nonlinear Anal. (T.M.A.), 20,823-833,1993
(31) N.Hayashi: Global existence of small solutions to quadratic nonlinear Schrödinger equations, Commun. P.D.E., 18, 1109-1124,1993
(32) N.Hayashi: Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain, Manuscript Math. 81, 15-39,1993


1994


(33) N.Hayashi: Global existence of small radially symmetric solutions to quadratic nonlinear evolution equations in an exterior domain, Math. Z., 215, 381-419,1994
(34) N.Hayashi and T.Ozawa: Remarks on nonlinear Schödinger equations in one space dimension, Differential and Integral Equations, 7, 453-461,1994
(35) N.Hayashi and T.Ozawa: Modified wave operators for the derivative nonlinear Schödinger equations, Math. Annalen, 298,557-576,1994
(36) N.Hayashi and T.Ozawa: Finite energy solutions of nonlinear Schrödinger equations of derivative type, SIAM J. Math. Anal.25, 1488-1503,1994


1995


(37) N.Hayashi and K.Kato: Regularity in time of solutions to nonlinear Schrödinger equations, J. Funct. Anal.128, 253-277,1995
(38) N.Hayashi and T.Ozawa: Global, small radially symmetric solutions to nonlinear Schrödinger equations and a gauge transformation, Diff. Integral Eqs. 8, 1061-1072,1995
(39) J.Ginibre and N.Hayashi: Almost global existence of small solutions to quadratic nonlinear Schrödinger equations in three space dimensions, Math. Z., 219, 119-140,1995
(40) N.Hayashi and J.C.Saut: Global existence of small solutions to the Davey-Stewartson and the Ishimori systems, Diff. Integral Eqs. 8,1657-1675,1995
(41) A.de Bouard, N.Hayashi and J.C.Saut: Sur une équation de Schrödiger non linéaire en physique relativiste, Compte rendus Acad. Sci. Paris t., 321, 175-178, 1995
(42) N.Hayashi: Global existence of small solutions to quadratic nonlinear wave equations in an exterior domain, J. Funct. Anal. , 131, 302-344,1995
(43) A. de Bouard, N. Hayashi and K. Kato: Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations, Ann. Henri Inst. Poincare Analyse nonlinear, 12,673-725, 1995
(44) N.Hayashi, K.Kato and T.Ozawa: Dilation method and smoothing effect of the Schrödinger evolution group, Reviews in Math. Phys.7, 1123-1132,1995
(45) N.Hayashi and T.Ozawa: Schr\"odinger equations with nonlinearity of integral type, Discrete and Continuous Dynamical Systems, 1, 475-484,1995


1996


(46) N.Hayashi: Global and almost global solutions to quadratic nonlinear Schrödinger equations with small initial data, Dynamics of Continuous, Discrete and Impulsive Systems, 2, 109-129,1996
(47) N.Hayashi, K.Kato and T.Ozawa: Dilation method and smoothing effect of solutions to the Benjamin-Ono equation, Proceedings of Royal Society of Edingburgh A, 126, 273-286,1996
(48) N.Hayashi: Local existence in time of solutions to higher order dispersive equations, Diff. Integral Eqs.9, 879-890,1996
(49) N.Hayashi and J.C.Saut: Global existence of small solutions to the Ishimori system without exponential decay on the data, Diff. Integral Eqs.,9,1183-1195,1996
(50) N.Hayashi and H.Hirata: Global existence and asymptotic behavior in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system, Nonlinearity, 9,1387-1409,1996
(51) N.Hayashi: Local existence in time of small solutions to the Davey-Stewartson system, Annales de l'I.H.P. Physique Theorique, 65, 313-366, 1996


1997


(52) N.Hayashi and K.Kato: Analyticity in time and smoothing effect of solutions to nonlinear Schrödinger equations, Commun. Math. Phys., 184 , 273-300,1997
(53) N.Hayashi and P.I.Naumkin: Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited, Discrete and Continuous Dynamical Systems, 3, 383-400,1997
(54) N.Hayashi and K.Kato: Global existence of small analytic solutions to Schrödinger equations with quadratic nonlinearity, Commun. In P.D.E., 22,773-798,1997
(55) A.de Bouard, N.Hayashi and J.C.Saut: Global existence of small solutions to a relativistic nonlinear Schrödinger equation, Commun. Math. Phys., 189,73-105,1997
(56) N.Hayashi and H.Hirata: Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space, Proceedings of the Edinburgh Mathematical Society, 40, 563-581, 1997
(57) N.Hayashi: Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data, J.Analysé Mathématique 73, 133-164, 1997


1998


(58) N.Hayashi and H.Hirata: Global existence of small solutions to nonlinear Schrödinger equations, Nonlinear Anal. (Theory Method Appl), 31, 671-685,1998
(59) N.Hayashi and P.I.Naumkin: Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation, Annales de l'I. H.P. Physique Theorique, 68,159-177,1998
(60) N.Hayashi and P.I.Naumkin: Asymptotics in large time of solutions to nonlinear Schrödinger and Hartree equations, Amer. J. Math., 120, 369-389,1998
(61) N.Hayashi, P.I.Naumkin and T.Ozawa: Scattering theory for the Hartree equation, SIAM J. Math. Anal., 29, 1256-1267,1998
(62) N. Hayashi and P.I. Naumkin: Remarks on Scattering theory and large time asymptotics of solutions to Hartree type equations with a long range potential SUT. J.Math., 34, 13-24,1998
(63) N. Hayashi and P.I. Naumkin: Large time asymptotics of solutions to the generalized Korteweg-de Vries equation J. Funct.Anal., 159, 110-136,1998
(64) N. Hayashi, E.I. Kaikina and P.I. Naumkin: On the scattering theory for the cubic nonlinear Schrödinger and Hartree type equations in one space dimension, Hokkaido Math. J., 27, 651-667,1998
(65) N. Hayashi and E.I. Kaikina: Local existence of solutions to the Cauchy problem for nonlinear Schrödinger equations, SUT J. Math., 34, 111-137,1998
(66) N. Hayashi, K.Kato and P.I. Naumkin: On the scattering in Gevrey classes for subcritical Hartree and Schrödinger equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , 27,483-497,1998


1999



(67) N.Hayashi and P.I.Naumkin: Large time asymptotics of solutions to the generalized Benjamin-Ono equation, Trans. Amer. Math. Soc., 351, 109-130,1999
(68) N. Hayashi, E.I. Kaikina and P.I. Naumkin: Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation, Discrete and Continuous Dynamical Systems, 5, 93-106,1999
(69) N. Hayashi, T.Matos and P.I. Naumkin: Large time behavior of solutions of higher - order nonlinear dispersive equations of KdV - type with weak nonlinearity, Diff. Integral Eqs.,12, 23-40,1999
(70) N. Hayashi and P.I. Naumkin: Large time behavior of solutions for the modified Korteweg-de Vries equation, International Mathematics Research Notices, 395-418,1999
(71)N. Hayashi, P.I. Naumkin and J.C. Saut: Large time behavior of solutions to the generalized Kadomtsev - Petviashvili equations, Commun. Math. Phys., 201, 577-590,1999
(72) N. Hayashi, P.I. Naumkin and P.N. Pipolo: Smoothing effects for some derivative nonlinear Schrödinger equations Discrete and Continuous Dynamical Systems, 5, 685-695,1999
(73) N. Hayashi and P.I. Naumkin: Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations without a self-conjugate property, Funkcialaj Ekvacioj, 42, 311-324,1999
(74) A.de Bouard, N.Hayashi, P.I.Naumkin and J.C.Saut: Scattering problem and asymptotics for a relativistic nonlinear Schrödinger equation, Nonlinearity, 12, 1415-1425,1999
(75)N.Hayashi, P.I.Naumkin and H.Uchida: Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations, Publ. RIMS, Kyoto Univ.,35, 501-513,1999
(76)N.Hayashi and P.I.Naumkin: On Davey-Stewartson and Ishimori systems, Mathematical Physics, Analysis and Geometry,2, 53-81,1999
(77)N.Hayashi, C.Miao and P.I.Naumkin: Global existence of small solutions to the generalized derivative nonlinear Schrödinger equations, Asymptotic Analysis,21, 133-147,1999


2000



(78) N.Hayashi and P.I.Naumkin: On the quadratic nonlinear Schrödinger equation in three space dimensions, International Mathematics Research Notices, 3, 115-132,2000
(79) N.Hayashi: Asymptotic behavior and global existence of small solutions to nonlinear wave equations in an exterior domain, Commun. P. D. E., 25, 423-456,2000
(80) N.Hayashi, P.I.Naumkin and P.N. Pipolo: Analytic smoothing effects for some derivative nonlinear Schrödinger equations, Tsukuba J. Math.24, 21-34,2000

(81) N.Hayashi, E.I.Kaikina and P.I.Naumkin: Large time behavior of solutions to the dissipative nonlinear Schrödinger equation, Proc. Royal Soc. Edinburgh, 130A, 1029-1043, 2000


2001


(82) N.Hayashi and P.I.Naumkin: Scattering theory and asymptotics for large time of solutions to the Hartree type equations with a long range potential, Hokkaido Math. J., 30, 137-161,2001

(83) N.Hayashi, E.I.Kaikina and F.R.Paredes: Boundary-value problem for the Korteweg-de Vries-Burgers type equation, NoDEA (Nonlinear Differential Equations and Applications), 8, 439-463, 2001

(84) N.Hayashi, E.I.Kaikina and P.I.Naumkin: Large time behavior of solutions to the Landau-Ginzburg type equations, Funkcialaj Ekvacioj, 44, 171-200, 2001

(85) N.Hayashi, P.I.Naumkin and Y.Yamazaki: Large behavior of small solutions to subcritical derivative nonlinear Schrödinger equations, Proc. Amer. Math. Soc., 130, 779-789, 2001

(86) N.Hayashi and P.I.Naumkin: Global existence of small solutions to the quadratic nonlinear Schrödinger equations in two space dimensions, SIAM J. Math. Anal. 32, 1390-1403, 2001

(87) N.Hayashi and P.I.Naumkin: Asymptotic behaviour for Schrödinger equations with a quadratic nonlinearity in one space dimension, Electron. J. Diff. Eqns. 54, 1-18, 2001

(88) N.Hayashi and P.I.Naumkin: On the modified Korteweg - de Vries equation, Mathematical Physics, Analysis and Geometry, 4, 197-227, 2001

(89) N.Hayashi, P.I.Naumkin  and Y.Yamazaki: Modified Scattering States of Small Solutions to Subcritical Derivative Nonliner Schrödinger Equations , Applicable Analysis , 80, 141-159, 2001


2002


(90) N.Hayashi, E.I.Kaikina and R.Manzo: Local and global existence of solutions to the nonlocal Whitham equation on half-line, Nonlinear Analysis, 48, 53-75, 2002

(91) N.Hayashi and P.I.Naumkin: On the reduction of the modified Benjamin - Ono equation to the cubic derivative nonlinear Schrödinger equation, Discrete Continuous Dynamical Systems, 8, 237-255, 2002

(92) N.Hayashi, P.I.Naumkin and H.Uchida: Analytic smoothing properties of global solutions for the elliptic-hyperbolic Davey-Stewartson system, Advances in Differential Equations, 7, 469-492, 2002

(93) N.Hayashi, E.I.Kaikina and I.A. Shishmarev: Asymptotics of solutions to the boundary-value problem for KdV-B equation on a half-line, Journal of Math. Anal. Appl., 265, 343-370, 2002

(94) N.Hayashi and  P.I.Naumkin : Asymptotic expansion of small solutions to the quadratic nonlinear  Schrödinger equations in two space dimensions, International Journal of Mathematics and Mathematical Sciences, 29, 501-516, 2002

(95) N.Hayashi and P.I.Naumkin: Large time behavior for the cubic nonlinear Schrödinger equation, Canadian Journal of Mathematics, 54, 1065-1085, 2002

(96) N.Hayashi, E.I.Kaikina and P.I.Naumkin: Asymptotic expansion of small solutions to the Landau-Ginzburg type equations,  Asymptotic Analysis, 32, 91-106, 2002

(97) N.Hayashi, E.I.Kaikina and H.F. Ruiz Paredes: Korteweg-de Vries-Burgers equation on a half-line with large initial data, J. Evolution Equations, 2 ,  319-347 , 2002

(98) N.Hayashi and  P.I.Naumkin: A quadratic nonlinear Schrödinger equation in one space dimension, J. Differential Equations, 186, 165-185, 2002

(99) N.Hayashi and P.I.Naumkin :  Asymptotics of small solutions to nonlinear Schrödinger equations  with cubic nonlinearities ,  International Journal of Pure and Applied Mathematics, 3, 255-273, 2002


2003


(100) N.Hayashi, T.Mizumachi and P.I.Naumkin: Time decay of small solutions to quadratic nonlinear Schrödinger equations in 3D, Differential Integral Equations, 16, 159-179, 2003

(101) N.Hayashi, E.I.Kaikina and P.I.Naumkin : Landau-Ginzburg type equations in the subcritical case, Communications Contemporary Mathematics ,5, 127-145, 2003

(102) N.Hayashi, E.I.Kaikina and J.L. Guardado Zavala : On the boundary-value problem for the Korteweg-de Vries equation, The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences, 459,  2861-2884, 2003

(103) N.Hayashi and P.I.Naumkin : Asymptotics for the Burgers equation with pumping, Commun. Math. Phys., 239, 287-307, 2003

(104) N.Hayashi, E.I.Kaikina and P.I.Naumkin : Global existence and time decay of small solutions to the Landau-Ginzburg type equations, J.Analys\'e Math\'ematique, 90, 141-173, 2003


2004


(105) N.Hayashi and E.I.Kaikina : Nonlinear Theory of Pseudodifferential Equations with a Half Line, North-Holland Mathematics Studies, Vol. 194, 340pp, ISBN 0-444-51569-0, 2004

(106) N.Hayashi, N.Ito, E.I.Kaikina and P.I.Naumkin: On some nonlinear dissipative equations with sub-critical nonlinearities, Taiwanese J. Math., 8, 135-154, 2004

(107) N.Hayashi and P.I.Naumkin: On the asymptotics for cubic nonlinear Schrödinger equations, Complex Variables, 49, 339-373, 2004

(108) N.Hayashi, N.Ito, E.I.Kaikina and P.I.Naumkin: Large time behavior of small solutions to Dirichlet problem for Landau-Ginzburg type equations, Funkcialaj Ekvacioj., 47, 479-497, 2004

(109) N.Hayashi, E.I.Kaikina and P.I.Naumkin: Asymptotics for critical non convective type equations, IJMMS, 2004:8, 377-405, 2004

(110) N.Hayashi, E.I.Kaikina and P.I.Naumkin: Damped wave equation in the subcritical case, J. Diff. Eqns,  207, 161-194, 2004

(111) N.Hayashi,  E.I.Kaikina and P.I.Naumkin : Damped wave equation with super critical nonlinearities, Diff. Integral Eqns. 17, 637-652, 2004

(112) N.Hayashi, P.I.Naumkin, A.Shimomura and S.Tonegawa : Modifed wave operators for nonlinear Schrödinger equations in one and two dimensions, Electron. J. Diff. Eqns., 62, 1-16, 2004

(113) N.Hayashi,  E.I.Kaikina and P.I.Naumkin :  Damped wave equation with a critical nonlinearity on a half line, J. Appl. Anal., 2, 95-112, 2004


2005


(114) N.Hayashi,  E.I.Kaikina and P.I.Naumkin : Asymptotics for sub critical non convective type equations, Mathematical Methods Applied Science, 28, 275-308, 2005

(115) N.Hayashi,  E.I.Kaikina, P.I.Naumkin and Isahi Sanchez-Suarez : Asymptotics for model nonlinear nonlocal equations, Diff. Integral Equations , 18, 1273-1298, 2005 

(116) N.Hayashi,  E.I.Kaikina and P.I.Naumkin : Asymptotics for fractional nonlinear heat equation, J.London Math. , 72, 663-688, 2005

(117) N.Hayashi, N.Ito, E.I.Kaikina and P.I.Naumkin : Large time decay of solutions to Burgers type equations, Applicable Anal., 84, no 10, 1005-1024, 2005   


2006


(118) N.Hayashi and  E.I.Kaikina : Neumann problem for the Korteweg-de Vries equation, J. Diff. Eqns,  225, 168-201, 2006

(119) N.Hayashi,  E.I.Kaikina and P.I.Naumkin : Damped wave equation with a critical nonlinearity, Trans. Amer. Math. Soc. , 358, 1165-1185, 2006

(120) N.Hayashi and P.I.Naumkin :  Asymptotics for the Korteweg-de Vries-Burgers equation, Acta Mathematica Sinica, 22, 1441-1456, 2006

(121) N.Hayashi,  Y.Kawahara and P.I.Naumkin :  Lower bounds of asymptotics in time of solutions to Nonlinear Schrödinger Equations in 3d, Nonlinear Analysis, 65, 1394-1410, 2006

(122) N.Hayashi and P.I.Naumkin : Asymptotics in time of solutions to nonlinear Schrödinger equations in two space dimensions, Funkcialaj Ekvacioj , 49, 415-425, 2006

(123) N.Hayashi,  E.I.Kaikina and  P.I.Naumkin : Asymptotics for critical Rosenau type equations with nonconvective nonlinearites on a half-line,  Complex Variables and Elliptic Equations, 51, 1153-1174, 2006

(124) N.Hayashi and  P.I.Naumkin : Domain and range of the modified wave operator for Schrödinger equations with a critical nonlinearity, Comm. Math. Phys., 267, 477-492, 2006

(125)    N.Hayashi and  P.I.Naumkin : Final state problem for Korteweg-de Vries type equations,  J. Math. Phys., 47, 123501,1-16, 2006

(126) Nakao Hayashi, Elena.I.Kaikina, Pavel I. Naumkin and Ilja A. Shishmarev  : Asymptotics for Dissipative Nonlinear Equations, Lecture Note in Mathematics, Springer Berlin Heidelberg New York, Vol. 1884, 557pp, ISBN 3-540-32059-8, 2006

 


2007


(127) N.Hayashi,  E.I.Kaikina and P.I.Naumkin : Asymptotics in the critical case for Whitham type equations, Nonlinear Analysis, 67, 2914- 2933, 2007

(128) N.Hayashi,  E.I.Kaikina and P.I.Naumkin :  Asymptotics for nonlinear damped wave equations with large initial data, Siberian Electronic Mathematical Reports, 4, 249-277, 2007

(129) N.Hayashi,  E.I.Kaikina and  P.I.Naumkin : Large time asymptotics for the BBM-Burgers equation, Ann. Henri Poincaré, 8, 485-511, 2007

(130) N.Hayashi,  E.I.Kaikina and  P.I.Naumkin : Subcritical nonlinear heat equation, J. Diff. Eqns, 238, 366-380, 2007

(131) N.Hayashi and P.I.Naumkin :  Existence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in 3d , Cubo. A Mathematical Journal, 9, 27-37, 2007

(132) N.Hayashi, E.I.Kaikina and  P.I.Naumkin : On the critical nonlinear damped wave equation with large initial data, J. Math. Anal. Appl., 334, 1400-1425, 2007

(133) N.Hayashi and  P.I.Naumkin : Nongauge invariant cubic nonlinear Schrödinger equations, Pacific Journal of  Applied Mathematics, 1, 27-43, 2007

(134) N.Hayashi and  P.I.Naumkin : Modified wave operators for nonlinear Schrödinger equations with subcritical dissipative nonlinearities, Inverse Problems and Imaging, 1 No. 2, 391-398, 2007


2008


(135) N.Hayashi and  P.I.Naumkin : Scattering operator for the nonlinear Klein-Gordon equations in higher space dimensions, J. Diff. Eqns., 244, 188-199, 2008

(136) N.Hayashi and  P.I.Naumkin : Asymptotics for a quadratic nonlinear Schrödinger equation, Electron. J. Diff. Eqns., No15, 38pp., 2008

(137) N.Hayashi and P.I.Naumkin :  Asymptotic properties of solutions to dispersive equation of Schrödinger type, J. Math. Soc. Japan, to appear

(138) N.Hayashi and  P.I.Naumkin : Scattering Operator for Nonlinear Klein-Gordon Equations, Communications in Contemporary Mathematics, to appear

(139) N.Hayashi and  P.I.Naumkin : The initial value problem and asymptotics of solutions for the cubic nonlinear Klein-Gordon equation, Zeitschrift fur Angewandte Mathematik und Physik, online

(140) N.Hayashi, H. Sunagawa and  P.I.Naumkin : On the Schrödinger equation with dissipative nonlinearities of derivative type, to appear in SIAM J. Math. Anal.

(141) N.Hayashi and P.I.Naumkin :  Nonlinear scattering for a system of  one dimensional nonlinear Klein-Gordon equations, to appear in Hokkaido Math. J

 


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