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 …

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 show how one can construct conservation laws of Euler-Lagrange-type equations via
Noether-type symmetry operators associated with what we term partial Lagrangians. This is …

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 …

Abstract This paper studies a (3+ 1)-dimensions extended quantum Zakharov–Kuznetsov
(qZK) equation. The quantum Zakharov–Kuznetsov (qZK) equation models several physical …

This study investigates the Slepyan–Palmov (SP) model, which describes plane longitudinal
waves propagating within a medium comprising a carrier medium and nonlinear oscillators …

This paper anatomizes the exact solutions of the resonant non-linear Schrödinger's equation
(R-NLSE) with the Kerr law non-linearity with the assistance of the new extended direct …