zbMATH — the first resource for mathematics

Integrable boundary-value problems and nonlinear Fourier harmonics. (English. Russian original) Zbl 0931.35160
J. Math. Sci., New York 77, No. 2, 3046-3050 (1995); translation from Zap. Nauchn. Semin. POMI 199, 43-50 (1992).
Summary: For the nonlinear Schrödinger equation, the integrable boundary-value problem on a segment is considered. The concept of nonlinear \(\theta\)-harmonics similar to the ordinary Fourier harmonics in the linear case is suggested. A solution of the initial boundary-value problem on the semiaxis is constructed by means of reduction to the Cauchy problem on the whole axis.

35Q55 NLS equations (nonlinear Schrödinger equations)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions