Abstract

This paper deals with localized waves in the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in the incompressible fluid. Based on Hirota’s bilinear method, N-soliton solutions related to Boiti–Leon–Manna–Pempinelli equation are constructed. Novel nonlinear wave phenomena are obtained by selecting appropriate parameters to N-soliton solutions, and time evolutions of different kinds of solitary waves are investigated in detail. Rich elastic interactions are illustrated analytically and graphically. More specifically, the inelastic interactions, i.e., fusion and fission of solitary waves, are constructed by choosing special parameters on kink solitons and breathers. The analysis of the influence of parameters on propagation is revealed in three tables. The results have potential applications in fluid mechanics.

中文翻译：

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（3 +1）维Boiti–Leon–Manna–Pempinelli方程的非线性局域共振和相互作用解

摘要

本文涉及不可压缩流体在（3 + 1）维Boiti–Leon–Manna–Pempinelli方程中的局域波。基于Hirota的双线性方法，构造了与Boiti–Leon–Manna–Pempinelli方程有关的N孤立子解。通过为N选择合适的参数可以获得新颖的非线性波现象-孤子解，以及不同种类的孤立波的时间演化被详细研究。分析和图形方式说明了丰富的弹性相互作用。更具体地说，通过选择扭结孤子和通气孔上的特殊参数来构造非弹性相互作用，即孤立波的融合和裂变。在三个表中显示了参数对传播的影响的分析。结果在流体力学中具有潜在的应用。