Asian Journal of Mathematics and Computer Research

The Reduction Transformation of the Generalized Variable-coefficient KdV Equation

Asian Journal of Mathematics and Computer Research, Volume 30, Issue 3, Page 30-38
DOI: 10.56557/ajomcor/2023/v30i38333

Abstract


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.

Keywords:
  • Variable-coefficient KdV equation;
  • modified CK direct method
  • reduction transformation
  • partial differential equation
  • solution of differential equations
  • integrable system

How to Cite

Chen, Y., & Liu, S. (2023). The Reduction Transformation of the Generalized Variable-coefficient KdV Equation. Asian Journal of Mathematics and Computer Research, 30(3), 30–38. https://doi.org/10.56557/ajomcor/2023/v30i38333

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