Abstract
In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended F-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.
Highlights
It is well-known that a lot of phenomena in many fields of science can be described by nonlinear evolution equations (NLEEs)
We know that Lie symmetry group [1] [2] is efficient to study NLEEs
A nonlinear wave solution of a higher-dimensional shallow water wave equation is discussed by Lie symmetry analysis combined with extending F-expansion method [3] [4]
Summary
It is well-known that a lot of phenomena in many fields of science can be described by nonlinear evolution equations (NLEEs). Lie symmetry group method has been applied in different fields and several physical models were studied In this manuscript, a nonlinear wave solution of a higher-dimensional shallow water wave equation is discussed by Lie symmetry analysis combined with extending F-expansion method [3] [4]. Study on nonlinear wave solution is few and Lie symmetry analysis on this equation is not given in related literatures. We want to get new nonlinear wave solutions of Equation (1) by investigate the reduced equations using extended F-expansion method. The symmetry group of Equation (1) will be generated by the vector field of the form (3). According to the Lie symmetry analysis method, the geometric vector fields of Equation (1) can be obtained as follows. V =V1 ( F1 ) +V2 ( F2 ) +V3 ( F3 ) +V4 ( F4 ) +V5 ( F5 ) +V6
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