https://doi.org/10.1140/epjp/s13360-020-00826-6
Regular Article
Closed form invariant solutions of (2+1)-dimensional extended shallow water wave equation via Lie approach
Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, India
a
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Received:
9
July
2020
Accepted:
1
October
2020
Published online:
10
October
2020
Abstract
In the present letter, some invariant solutions of (2+1)-dimensional extended shallow water wave equation are studied. We reduce the equation to an ordinary differential equation(ODE) via the Lie symmetry method. The similarity transformation method is used to determine the group-invariant solutions for the equation. The method plays an important role to reduce the number of independent variables by one in each stage and finally forms an ODE. On the other hand, solutions provide rich physical configuration due to the presence of some distinct arbitrary constants and functions. Furthermore, numerical simulation has been done to trace out the derived results which illustrate the dynamic behavior of these obtained solutions.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
