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New interaction solutions of the similarity reduction for the integrable (2+1)-dimensional Boussinesq equation
International Journal of Modern Physics B ( IF 1.7 ) Pub Date : 2021-11-27 , DOI: 10.1142/s0217979222500011
Hengchun Hu 1 , Xiaodan Li 1
Affiliation  

The nonlocal symmetry of the new integrable (2 + 1)-dimensional Boussinesq equation is studied by the standard truncated Painlevé expansion. This nonlocal symmetry can be localized to the Lie point symmetry of the prolonged system by introducing two auxiliary dependent variables. The corresponding finite symmetry transformation and similarity reduction related to the nonlocal symmetry of the new integrable (2 + 1)-dimensional Boussinesq equation are studied. The rational solution, the triangle solution, two solitoff-interaction solution and the soliton–cnoidal interaction solutions for the new (2 + 1)-dimensional Boussinesq equation are presented analytically and graphically by selecting the proper arbitrary constants.

中文翻译:

可积 (2+1) 维 Boussinesq 方程相似性约简的新交互解

新可积的非局部对称性(2 + 1)维 Boussinesq 方程通过标准截断 Painlevé 展开来研究。通过引入两个辅助因变量,可以将这种非局部对称性局部化为延长系统的李点对称性。与新可积的非局部对称性相关的相应有限对称变换和相似性降低(2 + 1)研究了维Boussinesq方程。新的有理解、三角形解、两个孤子相互作用解和孤子-cnoidal相互作用解(2 + 1)维 Boussinesq 方程通过选择适当的任意常数以解析和图形方式呈现。
更新日期:2021-11-27
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