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New Traveling Wave Solutions and Interesting Bifurcation Phenomena of Generalized KdV‐mKdV‐Like Equation

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  • Yiren Chen
  • Shaoyong Li

Abstract

Using the bifurcation method of dynamical systems, we investigate the nonlinear waves and their limit properties for the generalized KdV‐mKdV‐like equation. We obtain the following results: (i) three types of new explicit expressions of nonlinear waves are obtained. (ii) Under different parameter conditions, we point out these expressions represent different waves, such as the solitary waves, the 1‐blow‐up waves, and the 2‐blow‐up waves. (iii) We revealed a kind of new interesting bifurcation phenomenon. The phenomenon is that the 1‐blow‐up waves can be bifurcated from 2‐blow‐up waves. Also, we gain other interesting bifurcation phenomena. We also show that our expressions include existing results.

Suggested Citation

  • Yiren Chen & Shaoyong Li, 2021. "New Traveling Wave Solutions and Interesting Bifurcation Phenomena of Generalized KdV‐mKdV‐Like Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:4213939
    DOI: 10.1155/2021/4213939
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