Direct Reduction and Exact Solutions for Generalized Variable Coefficients 2D KdV Equation under Some Integrability Conditions

Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary different...

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Bibliographic Details
Published in:Communications in theoretical physics 2011-04, Vol.55 (4), p.551-554
Main Authors: Moussa, M.H.M, El-Shiekh, Rehab M
Format: Article
Language:English
Subjects:
Differential equations
Direct reduction
Exact solutions
Integral calculus
Integral equations
Mathematical analysis
Similarity
Two dimensional
二维KdV方程
变系数KdV方程
常微分方程
广义变系数
直接还原
精确行波解
精确解
齐次平衡
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Summary:Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary differential equation under some integrability conditions between the variable coefficients. Two different cases have been discussed, the search for solutions of those ordinary differential equations yielded many exact travelling and solitonic wave solutions in the form of hyperbolic and trigonometric functions under some constraints between the variable coefficients.
ISSN:0253-6102
DOI:10.1088/0253-6102/55/4/03