The Reduction Transformation of the Generalized Variable-coefficient KdV Equation
Asian Journal of Mathematics and Computer Research, Volume 30, Issue 3,
In this manuscript, we have studied the reduction transformation of the generalized variable-coefficient Korteweg-de Vries(KdV) equation by the modifed Clarkson-Kruskal(CK) direct method, and have established the connection between the generalized variable-coefficient KdV equation and the constant- coefficient KdV equation. After complicated calculations, a new transformation is obtained, which transforms the generalized one-dimensional KdV equation with variable-coefficients into the corresponding KdV equation with constant-coefficients. As we know, the new transformation has not been studied in current literature. Based on the transformation, the solution of variable-coefficient KdV equation can be obtained directly through the constant-coefficient KdV equation, and it is helpful to explore the similarity reduction and exact solution of variable-coefficient KdV equation. Furthermore, a special example is given to verify the correctness of the transformation we have proposed.
- Variable-coefficient KdV equation;
- modified CK direct method
- reduction transformation
- partial differential equation
- solution of differential equations
- integrable system
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