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Novel localized wave solutions of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation
Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2020-12-02 , DOI: 10.1088/1572-9494/abbbd8
Li Sun , Jiaxin Qi , Hongli An

Based on a special transformation that we introduce, the N-soliton solution of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed. By applying the long wave limit and restricting certain conjugation conditions to the related solitons, some novel localized wave solutions are obtained, which contain higher-order breathers and lumps as well as their interactions. In particular, by choosing appropriate parameters involved in the N-solitons, two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution. Five solutions including two breathers, two lumps, and interaction solutions between one breather and two bell-shaped solitons, one breather and one lump, or one lump and two bell-shaped solitons are constructed from the 4-soliton solution. Five interaction solutions mixed by one breather/lump and three bell-shaped solitons, two breathers/lumps and a bell-shaped soliton, as well as mixing with one lump, one breather and a bell-shaped soliton are constructed from the 5-soliton solution. To study the behaviors that the obtained interaction solutions may have, we present some illustrative numerical simulations, which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties. The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations. The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.



中文翻译:

(2 + 1)维Boiti–Leon–Manna–Pempinelli方程的新型局部波解

基于我们引入的特殊变换,构造了(2 + 1)维Boiti–Leon–Manna–Pempinelli方程的N孤立子解。通过应用长波极限并将某些共轭条件限制在相关孤子上,可以获得一些新颖的局部波解,其中包含高阶通气和团块以及它们之间的相互作用。特别是,通过选择N中涉及的适当参数-孤子,由3-孤子溶液构造了两个相互作用的溶液,它们由钟形孤子和一个呼吸器或钟形孤子和一个块混合。由4个孤子解决方案构造了五个解决方案,其中包括两个通气,两个块以及一个通气和两个钟形孤子之间的相互作用解决方案,一个通气和一个块状,或者一个块与两个钟形孤子之间的相互作用。由5个孤子构成五个交互解决方案,其中一个呼吸/块和三个钟形孤子,两个呼吸/块和一个钟形孤子混合,以及与一个块,一个呼吸器和一个钟形孤子混合。解决方案。为了研究所获得的相互作用解可能具有的行为,我们提供一些说明性的数值模拟,这表明参数的选择对解决方案的类型及其传播特性有很大的影响。所提出的方法可以有效地用于构造许多非线性演化方程的局部相互作用解。获得的结果可能有助于相关专家理解和研究非线性局部波在传播过程中的相互作用现象。

更新日期:2020-12-02
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