In this paper, we present a review of featured works in the field of hydrodynamics with the
main aim to clarify the ways of understanding the algorithms for solving the Navier–Stokes …

Since its birth in the 1920s, quantum mechanics has motivated and advanced the analysis of
linear operators. In this effort, it significantly contributed to the development of sophisticated …

The momentous revolution in science precipitated by Isaac Newton's calculus soon revealed
the central role of partial differential equations throughout mathematics and its manifold …

This book is a sequel to Symmetries and Integration Methods (2002), by George W. Bluman
and Stephen C. Anco. It includes a significant update of the material in the last three …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

The Lie symmetry technique is utilised to obtain three stages of similarity reductions, exact
invariant solutions and dynamical wave structures of multiple solitons of a (3+ 1) …

Nonlinear wave equations are generated by the elastic wave propagation through inelastic
material. We studied such a unidirectional nonlinear elastic wave by considering potential …

Since the early part of the 20th century, it has been understood that the description of nature
at the subatomic scale requires quantum mechanics. In quantum mechanics, the position …

In present work, new form of generalized fifth-order nonlinear integrable equation has been
investigated by locating movable critical points with aid of Painlevé analysis and it has been …