The Reduction Transformation of the Generalized Variablecoefficient KdV Equation
Asian Journal of Mathematics and Computer Research, Volume 30, Issue 3,
Page 3038
DOI:
10.56557/ajomcor/2023/v30i38333
Abstract
In this manuscript, we have studied the reduction transformation of the generalized variablecoefficient Kortewegde Vries(KdV) equation by the modifed ClarksonKruskal(CK) direct method, and have established the connection between the generalized variablecoefficient KdV equation and the constant coefficient KdV equation. After complicated calculations, a new transformation is obtained, which transforms the generalized onedimensional KdV equation with variablecoefficients into the corresponding KdV equation with constantcoefficients. As we know, the new transformation has not been studied in current literature. Based on the transformation, the solution of variablecoefficient KdV equation can be obtained directly through the constantcoefficient KdV equation, and it is helpful to explore the similarity reduction and exact solution of variablecoefficient KdV equation. Furthermore, a special example is given to verify the correctness of the transformation we have proposed.
 Variablecoefficient KdV equation;
 modified CK direct method
 reduction transformation
 partial differential equation
 solution of differential equations
 integrable system
How to Cite
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