Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition. (English) Zbl 1336.35326
Summary: This paper deals with a derivative nonlinear Schrödinger equation under periodic boundary conditions. Taking advantage of the symmetries of the equation, we search for the traveling wave solutions. The problem is reduced to second order nonlinear nonlocal differential equations. By solving the equations, explicit formulas for the traveling waves are obtained. These formulas allow us to visualize the global structure of the traveling waves with various speeds and profiles.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 35C07 | Traveling wave solutions |
| 33E05 | Elliptic functions and integrals |
Keywords:
derivative nonlinear Schrödinger equation; travelling waves; periodic boundary condition; elliptic functions; complete elliptic integrals; exact solutionReferences:
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