Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition

DOI10.3934/proc.2015.0878zbMath1336.35326OpenAlexW2324854686MaRDI QIDQ260925

Minoru Murai, Kunimochi Sakamoto, Shoji Yotsutani

Publication date: 22 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/proc.2015.0878

zbMATH Keywords

travelling wavesexact solutionperiodic boundary conditionelliptic functionsderivative nonlinear Schrödinger equationcomplete elliptic integrals

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Explicit solutions, first integrals of ordinary differential equations (34A05) Elliptic functions and integrals (33E05) Traveling wave solutions (35C07)

Related Items (3)

On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions ⋮ Representation formulas of solutions and bifurcation sheets to a nonlocal Allen-Cahn equation ⋮ Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation

Cites Work

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• Representation formula for the plane closed elastic curves
• Stability and bifurcation of periodic travelling waves in a derivative nonlinear Schrödinger equation
• On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows
• A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions
• On the Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition

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