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Exact integration of nonlinear Schrödinger equation. (English. Russian original) Zbl 0678.35012

Theor. Math. Phys. 74, No. 1, 20-32 (1988); translation from Teor. Mat. Fiz. 74, No. 1, 29-45 (1988).
Summary: By means of degeneration of general finite-gap formulas a many-parameter set of smooth periodic and almost-periodic solutions of the nonlinear Schrödinger equation expressed in terms of elementary functions is obtained. The scheme of obtaining these solutions by the method of the Darboux transformation is presented. The soliton propagation on arbitrary background is studied.

MSC:

35G20 Nonlinear higher-order PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35B10 Periodic solutions to PDEs
35B15 Almost and pseudo-almost periodic solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35J10 Schrödinger operator, Schrödinger equation
Full Text: DOI

References:

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