Abstract
Abstract In this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained. Furthermore, the conservation law is studied via the Ibragimov’s method.
Highlights
Nonlinear partial di erential equations (PDEs) arising in many physical elds like the condense matter physics, plasma physics, uid mechanics and optics and so on
In order to investigate the exact solution of PDEs, a fruitful techniques have been developed, such as traveling wave transformations, inverse scattering method [1], Darboux and Bäcklund transformations [2], Lie symmetry analysis [3,4,5]
Lie symmetry analysis is a very useful method to nd the new solutions of PDEs, which was distribution by Sophus Lie ( − )
Summary
Nonlinear partial di erential equations (PDEs) arising in many physical elds like the condense matter physics, plasma physics, uid mechanics and optics and so on. The optimal system and similarity reductions based on the Lie group method are obtained. In addition on the base of symmetries, the integrability of the nonlinear PDEs, such as group classi cation, optimal system and conservation laws, can be considered.
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