Exact soliton solutions of a \(D\)-dimensional nonlinear Schrödinger equation with damping and diffusive terms. (English) Zbl 1258.35181

Summary: In the present study, we apply function transformation methods to the \(D\)-dimensional nonlinear Schrödinger (NLS) equation with damping and diffusive terms. As special cases, this method applies to the sine-Gordon, sinh-Gordon, and other equations. Also, the results show that these equations depend on only one function that can be obtained analytically by solving an ordinary differential equation. Furthermore, certain exact solutions of these three equations are shown to lead to the exact soliton solutions of a \(D\)-dimensional NLS equation with damping and diffusive terms. Finally, our results imply that the planar solitons, \(N\) multiple solitons, propagational breathers, and quadric solitons are solutions to the sine-Gordon, sinh-Gordon, and \(D\)-dimensional NLS equations.


35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
Full Text: DOI


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