Periodic problem for the nonlinear Schroedinger equation
Vladimir Kotlyarov, Alexander Its
TL;DR
This paper introduces a method to find solutions to the nonlinear Schrödinger equation, including an algorithm for solving the periodic Cauchy problem with finite-gap initial conditions.
Contribution
It presents a novel constructive algorithm for solving the periodic nonlinear Schrödinger equation with finite-gap initial data.
Findings
Developed a new method for solution discovery.
Provided an algorithm for the periodic Cauchy problem.
Enhanced understanding of finite-gap solutions.
Abstract
The paper offers the method of discovering of some class of solutions for the nonlinear Schroedinger equation. An algorithm of constructive solving of the Cauchy periodic problem with a finite-gap initial condition was also obtained.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Nonlinear Waves and Solitons · Differential Equations and Boundary Problems