Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering

Chaudry Masood Khalique and Karabo Plaatjie
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Chaudry Masood Khalique: Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
Karabo Plaatjie: Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa

Mathematics, 2021, vol. 10, issue 1, 1-17

Abstract: In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form solutions of this model. The exact solutions obtained are the snoidal wave, cnoidal wave, Weierstrass elliptic function, Jacobi elliptic cosine function, solitary wave and exponential function solutions. Moreover, we give a graphical representation of the obtained solutions using certain parametric values. Furthermore, the conserved vectors of the underlying equation are constructed by utilizing two approaches: the multiplier method and Noether’s theorem. The multiplier method provided us with four local conservation laws, whereas Noether’s theorem yielded five nonlocal conservation laws. The conservation laws that are constructed contain the conservation of energy and momentum.

Keywords: generalized 2D equal-width equation; exact solution; Weierstrass elliptic functions; Kudryashov’s method; conservation laws; Noether’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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