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 …

In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that
models the wave pulse transmission in a time period less than one-trillionth of a second …

For systems of partial differential equations in three spatial dimensions, dynamical
conservation laws holding on volumes, surfaces, and curves, as well as topological …

For partial differential equations (PDEs) that have n≥ 2 independent variables and a
symmetry algebra of dimension at least n− 1, an explicit algorithmic method is presented for …

Conservation laws of the Hunter–Saxton equation for liquid crystal are constructed by using
multipliers. Based on the obtained conservation laws, we construct a tree of partial …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

Using underlying invariance/symmetry properties and related/associated conservation laws,
we investigate some'high'order nonlinear equations. The multiplier method is mainly used to …

A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are
shown to be a special case of a standard formula that uses a pair consisting of a symmetry …

Nonlinear generalizations of integrable equations in one dimension, such as the Korteweg–
de Vries and Boussinesq equations with p-power nonlinearities, arise in many physical …

In this article, we investigate two types of double dispersion equations in two different
dimensions, which arise in several physical applications. Double dispersion equations are …