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Integrable nonlinear equations on a half-axis

Research paper by L. A. Sakhnovich

Indexed on: 01 Nov '91Published on: 01 Nov '91Published in: Ukrainian Mathematical Journal



Abstract

A study is made of the nonlinear Schrödinger equation and the modified Kortewegde Vries equation on the half-axis 0≤x<∞. Classes of solutions are identified when there is sufficient initial data for unique solvability of a corresponding problem. The class of solutions investigated is characterized in terms of the Weyl-Titchmarsh function of an auxiliary linear problem. A solution is constructed in explicit form when the corresponding Weyl-Titchmarsh function v(t, z) is a rational function of z.