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Zbl 1162.35449
Sayed, S.M.; Elhamahmy, O.O.; Gharib, G.M.
Travelling wave solutions for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations which describe pseudospherical surfaces. (English)
[J] J. Appl. Math. 2008, Article ID 576783, 10 p. (2008). ISSN 1110-757X; ISSN 1687-0042/e

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 2000:: *35Q53 KdV-like equations
35Q55 NLS-like (nonlinear Schroedinger) equations
35A30 Geometric theory for PDE, transformations
53C44 Geometric evolution equations (mean curvature flow)

Keywords: KdV-Burgers-Kuramoto equation; nonlinear Schrödinger equation; pseudospherical surfaces

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Zentralblatt MATH Berlin [Germany]