## Formulation of scattering theory for the nonlinear Schrödinger equation with boundary conditions of the finite density type in a soliton-free sector.(English. Russian original)Zbl 0724.35082

J. Sov. Math. 54, No. 3, 900-905 (1991); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 169, 60-67 (1988).
See the review in Zbl 0695.35145.

### MSC:

 35P25 Scattering theory for PDEs 81U20 $$S$$-matrix theory, etc. in quantum theory 35Q55 NLS equations (nonlinear Schrödinger equations)

### Keywords:

nonlinear Schrödinger equation; finite density

### Citations:

Zbl 0651.35015; Zbl 0618.35100; Zbl 0695.35145
Full Text:

### References:

 [1] L. A. Takhtadzhyan and L. D. Faddeev, Hamiltonian Approach to the Theory of Solitons [in Russian], Moscow (1986). · Zbl 0632.58003 [2] B. S. Buslaev, L. D. Faddeev, and L. A. Takhtadzhyan [Takhtajan], ?Scattering theory for the Korteweg-de Vries (KdV) equation and its Hamiltonian interpretation,? Physica D,18, 235?266 (1986). · Zbl 0618.35100 [3] A. R. Its and A. F. Ustinov, ?Temporal asymptotic behavior of the solution of the Cauchy problem for the nonlinear Schrödinger equation with boundary conditions of the finite density type,? Dokl. Akad. Nauk SSSR,291, No. 1, 91?95 (1986). · Zbl 0651.35015
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