Integrability and beyond. (English. Russian original) Zbl 0932.37061

Fokas, A. S.

J. Math. Sci., New York 94, No. 4, 1593-1599 (1999); translation from Zap. Nauchn. Semin. POMI 235, 235-244 (1996).

Summary: An algebraic approach to solving nonlinear functional equations in the Riemann theta functions is stated. By the inverse scattering method and some general methods of the theory of partial differential equations, the solution of the initial boundary value problem for the nonlinear Schrödinger equation is presented.

MSC:

37K15	Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K20	Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Keywords:

inverse spectral method; nonlinear functional equations; Riemann theta functions; inverse scattering method; initial boundary value problem; nonlinear Schrödinger equation

Citations:

Zbl 0924.00015

References:

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