Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

We perform complete group classification of the general class of quasi linear wave
equations in two variables. This class may be seen as a broad generalization of the …

A complete group classification of a class of variable coefficient (1+ 1)-dimensional
telegraph equations f (x) utt=(H (u) ux) x+ K (u) ux⁠, is given, by using a compatibility …

We perform complete group classification of the general class of quasilinear wave equations
in two variables. This class may be seen as a generalization of the nonlinear d'Alembert …

General results are given for the forms of infinitesimal point symmetries of the class of partial
differential equations in which utt is a function of x, t, u, ut and the x-derivatives of u up to …

Given a class F(θ) of differential equations with arbitrary element θ, the problems of
symmetry group, nonclassical symmetry and conservation law classifications are to …

In this paper, complete group classification of a class of (1+ 1)-dimensional generalized
quasi-linear wave equations is performed by using the Lie–Ovsiannikov method, additional …

Reduction operators, ie, the operators of nonclassical (or conditional) symmetry of a class of
variable coefficient nonlinear wave equations with power nonlinearities, are investigated …

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation
with both second-order and fourth-order wave terms, which is extended from the classical …

A classification is given for the nonlinear wave equation utt= f (x, u) uxx+ g (x, u) admitting an
extension by one dimension of the principal Lie algebra of the equation under consideration …