I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

The nonlocal symmetries for the (2+ 1)(2+ 1)-dimensional Konopelchenko–Dubrovsky
equation are obtained with the truncated Painlevé method and the Möbious (conformal) …

We use the method of Lie symmetry analysis to investigate the properties of a (2+ 1)-
dimensional KdV–mKdV equation. Using the Ibragimov method, which relies only on the …

Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and
applying methods of generalized and functional separation of variables used to find exact …

We compute nonlocal symmetries and obtain kink type soliton solutions to an integrable
soliton equation. We construct a tree of nonlocally related partial differential equations …

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 …

Symmetry-and conservation law-preserving finite difference discretizations are obtained for
linear and nonlinear one-dimensional wave equations on five-and nine-point stencils using …

In this work, the tanh method is employed to compute some traveling wave patterns of the
nonlinear third-order (2+ 1) dimensional Chaffee-Infante (CI) equation. The tanh technique …

This review begins with the standard Lie symmetry theory for nonlinear PDEs and explores
extensions of symmetry analysis. First, it introduces three key symmetry reduction methods …

The paper is concerned with different classes of nonlinear Klein–Gordon and telegraph type
equations with variable coefficients c (x) utt+ d (x) ut=[a (x) ux] x+ b (x) ux+ p (x) f (u), where f …