The conservation laws for second order scalar partial differential equations and systems of
partial differential equations which occur in fluid mechanics are constructed using different …

Lie symmetry analysis of differential equations provides a powerful and fundamental
framework to the exploitation of systematic procedures leading to the integration by …

In this manuscript, the Lie point symmetries, conservation laws, and traveling wave
reductions have all been derived. Also, new forms of soliton solutions of generalized q …

In this study, we have dealt with a wave equation containing 4th order nonlinear mixed
derivative. This model corresponds to solitary waves in nonlinear elastic circular rod. One …

This paper studies the integrable Kuralay equation which is a kind of integrable spin system
in (1+ 1) dimensions. Several new exact solutions of different kinds such as optical solitons …

This paper gives a general treatment and proof of the direct conservation law method
presented in Part I (see Anco & Bluman [3]). In particular, the treatment here applies to …

Symmetry methods are always very useful for discussing the classes of differential equation
solutions. This article focuses on traveling wave structures of the generalized Pochhammer …

A general method using multipliers for finding the conserved integrals admitted by any given
partial differential equation (PDE) or system of partial differential equations is reviewed and …

We present a recently developed Maple-based “GeM” software package for automated
symmetry and conservation law analysis of systems of partial and ordinary differential …

We investigate stationary spatially localized hexagon patterns of the two-dimensional (2D)
Swift–Hohenberg equation in the parameter region where the trivial state and regular …