Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (4): 1-10.doi: 10.3969/j.issn.1000-5641.2023.04.001

• Mathematics •     Next Articles

New types of solitons and multiwave solutions for two higher-dimensional nonlinear evolution equations with time-dependent coefficients

Yuxin QIN1, Yinping LIU2,*(), Guiqiong XU3   

  1. 1. School of Computer Science and Technology, East China Normal University, Shanghai 200062, China
    2. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
    3. School of Management, Shanghai University, Shanghai 200444, China
  • Received:2022-01-18 Online:2023-07-25 Published:2023-07-25
  • Contact: Yinping LIU


Linear traveling-wave transformations are usually applied when constructing exact traveling-wave solutions for nonlinear evolution equations. Herein, for the first time, specific nonlinear traveling-wave transformations are introduced to extend the $N$ -soliton decomposition algorithm and an inheritance-solving strategy to a variable-coefficient nonlinear evolution equation. Two higher-dimensional nonlinear evolution equations with time-dependent coefficients, the Boiti-Leon-Manna-Pempinelli (BLMP) equation and the cylindrical Kadomtsev-Petviashvili (cKP) equation, are solved. The direct algebraic method and inheritance-solving strategy are used to construct several different types of multiwave-interaction solutions for the BLMP equation, specifically, the horseshoe-like solitons and their interaction with lump as well as different periodic waves. Using the $N$ -soliton decomposition algorithm, the higher-order interaction solutions between the horseshoe-like solitons, breathers, and lump waves of the cKP equation are established. These new multiwave-interaction solutions contribute to the existing solutions of nonlinear evolution equations with variable coefficients, enriching the repository of solutions to a certain extent.

Key words: Boiti-Leon-Manna-Pempinelli equation, cylindrical Kadomtsev-Petviashvili equation, multiwave-interaction solution, horseshoe-like soliton, time-dependent coefficient

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