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Exact Solutions for a Generalized KdV-MKdV Equation with Variable Coefficients

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  • Bo Tang
  • Xuemin Wang
  • Yingzhe Fan
  • Junfeng Qu

Abstract

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of variable-coefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for the KdV-MKdV equation are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving many other nonlinear partial differential equations with variable coefficients in mathematical physics.

Suggested Citation

  • Bo Tang & Xuemin Wang & Yingzhe Fan & Junfeng Qu, 2016. "Exact Solutions for a Generalized KdV-MKdV Equation with Variable Coefficients," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, February.
    • Handle: RePEc:hin:jnlmpe:5274243
    DOI: 10.1155/2016/5274243
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