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

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  • 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.
    Mathematics Subject Classification: Primary: 35Q55, 34A05; Secondary: 34B15.


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