On the similarity solutions and conservation laws of the Cooper‐Shepard‐Sodano equation

Abstract

In this paper, for the Cooper‐Shepard‐Sodano equation, some conservation laws are obtained by applying the multiplier method. Furthermore, we study this equation from the point of view of Lie symmetries. We perform an analysis of the symmetry reductions taking into account the similarity variables and the similarity solutions, which allow us to transform our equation into ordinary differential equations.

Conservation laws and exact series solution of fractional‐order Hirota–Satsuma‐coupled Korteveg–de Vries system by symmetry analysis

“…Singla and Gupta 41 extended the symmetry approach from single-time FPDEs to nonlinear system of time FODEs. Noether's theorem [42][43][44][45] established a relation between conservation laws and symmetry of differential equations and applied on FPDEs without Lagrangian operators.…”

Invariant analytical solutions for the motion of an elastic string with electric current in a static magnetic field

“…The modern group theory analysis of differential equations is a powerful tool to find analytical solutions for complicated systems of differential equations that describe natural phenomena. As recent advances in this field, we refer to the works on gas dynamics, 1 fluid mechanics, 2,3 epidemiology, 4 economy sciences, 5,6 plasticity, 7 nonlinear equations of Korteweg‐de Vries type, 8,9 variable‐coefficient Burgers equations, 10 and generalized Benney system 11 …”

Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion

“…The research of Lie symmetries of PDEs may allow to construct invariant solutions, reduce the number of independent variables, reduce the PDE to ordinary differential equations (ODE) or reduce the order of the ODE, among others. Therefore, symmetries have become a powerful tool in the study of PDE [14,15,16,22].…”

“…The research of Lie symmetries of PDEs may allow to construct invariant solutions, reduce the number of independent variables, reduce the PDE to ordinary differential equations (ODE) or reduce the order of the ODE, among others. Therefore, symmetries have become a powerful tool in the study of PDE [14,15,16,22]. Lie method is a systematic method that allows to obtain all the Lie symmetries for a given equation, including those that only occur for some specific function f .…”