Interaction Equations for Short and Long Dispersive Waves
Tài liệu tham khảo
Bekiranov, 1996, On the well-posedness of Benney's interaction equation of short and long waves, Advances Diff. Equations, 1, 919
Bekiranov, 1997, Weak solvability and well posedness of the coupled Schrödinger Korteweg-de Vries equations in the capillary-gravity interaction waves, Proc. Amer. Math. Soc., 125, 2907, 10.1090/S0002-9939-97-03941-5
Benilov, 1983, To the integrability of the equations describing the Langmuir-wave-ion-wave interaction, Phys. Let., 98A, 256, 10.1016/0375-9601(83)90865-4
Benjamin, 1967, Internal waves of permanent form in fluids of great depth, J. Fluid Mech., 29A, 559, 10.1017/S002211206700103X
Benney, 1976, Significant interactions between small and large scale surface waves, Stud. Appl. Math., 55, 93, 10.1002/sapm197655293
Benney, 1977, A general theory for interactions between short and long waves, ibid., 56, 81
Bourgain, 1993, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I Schrödinger equations, Geometric and Funct. Anal., 3, 107, 10.1007/BF01896020
Bourgain, 1993, Exponential sums and nonlinear Schrödinger equations, ibid., 3, 157
Bourgain, 1993, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II The KdV equation, ibid., 3, 209
Bourgain, 1994, On the Cauchy and invariant measure problem for the periodic Zakharov system, Duke Math. J., 76, 175, 10.1215/S0012-7094-94-07607-2
Cazenave, 1990, The Cauchy problem for the critical nonlinear Schrödinger equation inHs, Nonlinear Anal. T.M.A., 100, 807, 10.1016/0362-546X(90)90023-A
Djordjevic, 1977, On two-dimensional packet of capillary-gravity waves, J. Fluid Mech., 79, 703, 10.1017/S0022112077000408
Funakoshi, 1983, The resonant interaction between a long internal gravity wave and a surface gravity wave packet, J. Phys. Soc. Japan, 52, 1982, 10.1143/JPSJ.52.1982
Ginibre, 1994, Le problème de Cauchy pour des edp semi-linéaires périodiques en variables d'espace [d'apès Bourgain], Séminaire BOURBAKI, 47, 1
Ginibre, 1997, On the Cauchy problem for the Zakharov system, J. Funct. Anal., 151, 384, 10.1006/jfan.1997.3148
Ginibre, 1991, Smoothing properties and existence of solutions for the generalized Benjamin-Ono equation, J. Differential Equations, 93, 150, 10.1016/0022-0396(91)90025-5
Grimshaw, 1977, The modulation of an interval gravity-wave packet and the resonance with the mean motion, Stud. Appl. Math., 56, 241, 10.1002/sapm1977563241
Hayashi, 1993, The initial value problem for the derivative nonlinear Schrödinger equation, Nonlinear Anal. TMA., 20, 823, 10.1016/0362-546X(93)90071-Y
Hayashi, 1996, Dilation method and smoothing effects of solutions to the Benjamin-Ono equation, Proc. Roy. Soc. Edinburgh, 126A, 273, 10.1017/S0308210500022733
Hayashi, 1994, Modified wave operators for the derivative nonlinear Schrödinger equation, Math. Annalen, 298, 557, 10.1007/BF01459751
Iorio, 1986, On the Cauchy problem for the Benjamin-Ono equation, Comm. P.D.E., 11, 1031, 10.1080/03605308608820456
Karpman, 1975, On the dynamics of sonic-Langmuir soliton, Physica Scripta, 11, 263, 10.1088/0031-8949/11/5/003
Kato, 1987, On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique théorique, 46, 113
Kawahara, 1975, Nonlinear interaction between short and long capillary-gravity waves, J. Phys. Soc. Japan, 39, 1379, 10.1143/JPSJ.39.1379
Kenig, 1993, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J., 71, 1, 10.1215/S0012-7094-93-07101-3
Kenig, 1994, On the generalized Benjamin-One equation, Trans. Amer. Math. Soc., 342, 155, 10.1090/S0002-9947-1994-1153015-4
Kenig, 1996, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9, 573, 10.1090/S0894-0347-96-00200-7
Kenig, 1996, Quadratic forms for the 1-D semilinear Schrödinger equation, Trans. Amer. Math. Soc., 348, 3323, 10.1090/S0002-9947-96-01645-5
Laurençot, 1995, On a nonlinear Schrödinger equation arising in the theory of water waves, Nonlinear Anal. TMA, 24, 509, 10.1016/0362-546X(94)00106-R
Ma, 1978, The complete solution of the long-wave-short-wave resonance equations, Stud. Appl. Math., 59, 201, 10.1002/sapm1978593201
Ono, 1975, Algebraic solitary waves in stratified fluids, J. Phys. Soc. Japan, 39, 1082, 10.1143/JPSJ.39.1082
Ogawa, 1997, Global well-posedness and conservation law of the water wave interaction equation, Proc. Roy. Soc. Edinburgh Ser. A, 172, 369, 10.1017/S0308210500023684
T. Ozawa, On the nonlinear Schrödinger equations of derivative type
Ponce, 1991, On the global well-posedness of the Benjamin-Ono equation, Diff. Integral Equations, 4, 542
Staffilani, 1997, Quadratic forms for a 2-D semilinear Schrödinger equation, Duke Math. J., 86, 79, 10.1215/S0012-7094-97-08603-8
Strichartz, 1977, Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equation, Duke Math. J., 44, 705, 10.1215/S0012-7094-77-04430-1
Tsutsumi, 1993, Well-posedness of the Cauchy problem for a coupled Schrödinger-KdV equation, Math. Sci. Appl., 2, 513
Tsutsumi, 1994, Well-posedness of the Cauchy problem for long wave-short wave resonance equation, Nonlinear Anal. TMA, 22, 155, 10.1016/0362-546X(94)90032-9
Tsutsumi, 1994, Well-posedness of the Cauchy problem for Benney's first equations of long wave short wave interactions, Funkcialaj Ekvacioj, 37, 289
Tsutsumi, 1987, L2, Funkcialaj Ekvacioj, 30, 115
Yajima, 1976, Formation and interaction of sonic-Langmuir soliton, Progr. Theor. Phys., 56, 1719, 10.1143/PTP.56.1719
Yajima, 1979, Soliton solutions in a diatomic lattice system, Prog. Theor. Phys., 62, 370, 10.1143/PTP.62.370
Zakharov, 1972, Exact theory of two-dimensional self-focusing and one-dimensional self modulation of waves in nonlinear media, Sov. Phys. JETP, 34, 62