## 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

### Citations:

Zbl 0514.35077; Zbl 0513.35011; Zbl 0559.35074
Full Text:

### References:

 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.