Lie Symmetry Reductions and Wave Solutions of Coupled Equal Width Wave Equation
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Lie Symmetry Reductions and Wave Solutions of Coupled Equal Width Wave Equation Swati Chauhan1
· Rajan Arora1 · Antim Chauhan1
Accepted: 15 October 2020 © Springer Nature India Private Limited 2020
Abstract In the present paper, we have solved the coupled equal width wave equation by using the Lie symmetry analysis method. By applying the Lie symmetry transformation to the system of non-linear partial differential equations, we obtained the infinitesimal generators to the system and converted the system of non-linear partial differential equations into the system of nonlinear ordinary differential equations. Further, the obtained system of ordinary differential equations has been solved by using the tanh method and power series method. The travelling wave solution to the coupled equal width wave equation has also been obtained. We have also found some implicit solution to the coupled equal width wave equation. The convergences of power series solutions have been shown. Keywords Lie symmetry analysis · Coupled equal width wave equation · Similarity solutions · Tanh method · Power series solution
Introduction The world around us can be described by the model of non-linear partial differential equations. To express complex physical phenomena in the different fields of science such as solid-state physics, fluid mechanics, chemical physics, plasma physics, nonlinear optics, surface wave in compressible fluids etc., non-linear evolution equations are widely used. The study of non-linear equations has received much attention from mathematicians and physicists due to their wide applicability in various fields. In past few decades, the researchers encounter problems in gaining a better understanding of mathematical models formulated in terms of non-linear partial differential equations (NPDEs). It is well known that great endeavour has been made to get effective methods to find the exact solutions of NPDEs. The exact solutions
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Swati Chauhan [email protected] Rajan Arora [email protected] ; [email protected] Antim Chauhan [email protected] ; [email protected]
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Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India 0123456789().: V,-vol
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Int. J. Appl. Comput. Math
(2020) 6:159
of NPDEs provide us more information to understand and get better vision for the complex physical phenomena associated with it. Furthermore, the study of NPDEs is extended to the system of NPDEs. Recently, many methods were developed to solve these systems; for example: sine-cosine function method [1,2], homotopy perturbation method [3,4], extended tanh function method [2,5,6], (G’/G)-expansion method [7,8] and so on. Regularised long wave (RLW) [9] equation has solitary wave solutions while Equal Width Wave (EWW) equation also has solitary wave solutions, but of a less general type. The Equal Width Wave (EWW) equation characterized the nature of non-linear dispersive waves in many regions like an ion-acoustic wave in plasma, cold plasma, shallow
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