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Asymptotic behavior for t\(\to \infty\) of the solutions of the equation \(\psi _{xx}+u(x,t)\psi +(\lambda /4)\psi =0\) with a potential u, satisfying the Korteweg-de Vries equation. II. (English) Zbl 0582.35009

Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 138, 8-32 (Russian) (1984; Zbl 0559.35074).

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35J10 Schrödinger operator, Schrödinger equation
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[1] V. E. Zakharov and S. V. Manakov, ?The 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).
[2] M. J. Ablowitz and H. Segur, ?Asymptotic solutions of the Korteweg-de Vries equation,? Stud. Appl. Math.,57, 13?44 (1977). · Zbl 0369.35055
[3] V. S. Buslaev and V. V. Sukhanov, ?The asymptotic behavior of the solutions of the Korteweg-de Vries equation for long time,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,120, 35?39 (1982). · Zbl 0514.35077
[4] C. S. Gardner, J. M. Greene, 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
[5] V. S. Buslaev and V. V. Sukhanov, ?On the asymptotic behavior as t ? ? of the solutions of the equation ?xx+u?+?/4?=0 with a potential u satisfying the Korteweg-de Vires equation. I,? Probl. Mat. Fiz., No. 10, 70?102 (1982). · Zbl 0513.35011
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