Group-invariant solutions to $$SL'(2)$$-motion equation

Gao, Fang; Niu, Zhenjie; Wang, Z

doi:10.1007/s12043-021-02140-x

Cited by 1 publication

(1 citation statement)

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“…Obtaining group invariant solutions by Lie symmetry analysis is not only significant for the physical model itself [10], but also provides a basis for the problem of accuracy of numerical and approximate treatments. However, in the process of finding the exact solutions of some NLPDEs, there is the problem of complex calculation steps and large calculation amount, which requires an effective systematic method to classify some equivalent solutions, resulting in the optimal system [11][12][13]. The equivalence relations are gotten through the optimal system, which classifies all the group invariant solutions on the equivalence relations basis and selects each type of representative for similarity reduction, the dimension reduction equation will be obtained.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis, optimal system and exact solutions for variable-coefficients Boiti-Leon-Manna-Pempinelli equation

Yang,

Jin,

Xin

2024

Phys. Scr.

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In this paper, the constant coefficients are extended to variable coefficients in the Boiti-Leon-Manna-Pempinelli(BLMP) equation, and its optimal system, exact solutions, conservation laws are studied. First, the infinitesimal generators for independent variables of the variable-coefficient Boiti-Leon-Manna-Pempinelli(vcBLMP) equation are solved by using the Lie symmetry analysis method. Subsequently, the optimal system of the vcBLMP equation is solved, and then the equations are subjected to similarity reduction, the partial differential equations(PDEs) are gained. Based on these PDEs, the representative equations are converted into ordinary differential equations(ODEs) by traveling wave transformation, and some new exact solutions of vcBLMP equation is obtained by using G ′ / G − expansion method and tanh-function method, such as the kink solutions, periodic solutions and soliton solutions. According to the obtained solutions, the corresponding images are plotted in order to facilitate the presentation of structural features of the solutions. At the end, the vcBLMP equation is proved to be nonlinear self-adjoint equation and the conservation laws of vcBLMP are solved.

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