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Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times. (English) Zbl 0597.35102

Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 120, 32-50 (Russian) (1982; Zbl 0514.35077).

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B40 Asymptotic behavior of solutions to PDEs

Citations:

Zbl 0514.35077
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References:

[1] V. S. Buslaev and V. V. Sukhanov, ?On the asymptotic behavior as t ? ? of solutions of the equations ?XX + u? + ??/4=0 with a potential satisfying the Korteweg-de Vries equation,? in: Probl. Mat. Fiz., Vol. 10, Leningrad State Univ. (1982), pp. 70?102. · Zbl 0513.35011
[2] V. E. Zakharov and S. V. Manakov, ?Asymptotic behavior of nonlinear wave systems integrable by the method of the inverse scattering problem,? Zh. Eksp. Teor. Fiz.,71, No. 1, 203?215 (1976).
[3] V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons. The Method of the Inverse Problem [in Russian], Moscow (1980). · Zbl 0598.35002
[4] M. J. Ablowitz and H. Segur, ?Asymptotic solutions of the Korteweg-de Vries equation,? Stud. Appl. Math.,57, 13?44 (1977). · Zbl 0369.35055
[5] C. S. Gardner, J. M. Green, M. D. Kruskal, and R. M. Miura, ?Method for solving the Korteweg-de Vries equation,? Phys. Rev. Lett.,19, 1095?1097 (1967). · Zbl 1061.35520
[6] V. Yu. Novokshenov, ?Asymptotics as t ? ? of the solution of the Cauchy problem for the nonlinear Schrodinger equation,? Dokl. Akad. Nauk SSSR,251, No. 4, 799?802 (1980). · Zbl 0455.35047
[7] V. S. Buslaev, ?Use of the determinant representation of solutions of the Kortewegde Vries equation for investigation of their asymptotic behavior for large times,? Usp. Mat. Nauk,36, No. 4, 217?218 (1981).
[8] A. R. Its, ?Asymptotics of solutions of the nonlinear Schrödinger equation and isomonodromic deformations of systems of linear differential equations,? Dokl. Akad. Nauk SSSR,261, No. 1, 14?18 (1981). · Zbl 0534.35028
[9] V. S. Buslaev and V. B. Matveev, ?Wave operators for the Schrödinger equation with a slowly decaying potential,? Teor. Mat. Fiz.,2, No. 3, 367?376 (1970).
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