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 …

The general concept of nonlinear self-adjointness of differential equations is introduced. It
includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self …

The direct method for the construction of local conservation laws of partial differential
equations (PDE) is a systematic method applicable to a wide class of PDE systems (S. Anco …

An effective algorithmic method is presented for finding the local conservation laws for
partial differential equations with any number of independent and dependent variables. The …

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 …

The calculus of variations has a long history of interaction with other branches of
mathematics such as geometry and differential equations, and with physics, particularly …

Under investigation in this work is a generalized higher-order beam equation, which is an
important physical model and describes the vibrations of a rod. By considering Lie symmetry …

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 …

This paper investigates the exact invariant solutions and the dynamics of soliton solutions to
the (2+ 1)-dimensional generalized Hirota–Satsuma–Ito (g-HSI) equations. By applying the …