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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) Zbl 1162.35449

J. Appl. Math. 2008, Article ID 576783, 10 p. (2008).
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.

Cited in 7 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)

Keywords:

KdV-Burgers-Kuramoto equation; nonlinear Schrödinger equation; pseudospherical surfaces
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\textit{S. M. Sayed} et al., J. Appl. Math. 2008, Article ID 576783, 10 p. (2008; Zbl 1162.35449)
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References:

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