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Travelling wave solutions for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations which describe pseudospherical surfaces. (English) Zbl 1162.35449
Summary: We use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations with constant Gaussian curvature $ - 1$. Travelling wave solutions for the above equations are obtained by using a sech-tanh method and Wu’s elimination method.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
35A30Geometric theory for PDE, characteristics, transformations
53C44Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
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Full Text: DOI EuDML
References:
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