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 …

In this article, we construct exact solutions to a quasilinear system of hyperbolic partial
differential equations which governs the dynamics of a thin film of a perfectly soluble anti …

In this paper, we study the novel nonlinear wave structures of a (2+ 1)-dimensional variable-
coefficient Korteweg–de Vries (KdV) system by its analytic solutions. Its N-soliton solutions …

We consider nonlinear wave type PDEs with delay of the form ut t+ H 1 (u) ut=[G (u) ux] x+ H
2 (u) u x+ F (u, w), where u= u (x, t) is the unknown function, w= u (x, t− τ), and τ is the delay …

Any partial differential equation (PDE) system can be effectively analyzed through
consideration of its tree of nonlocally related systems. If a given PDE system has n local …

An algorithmic framework is presented to find an extended tree of nonlocally related systems
for a given system of differential equations (DEs). Each system in an extended tree is …

Two formulas are introduced to directly obtain new conservation laws for any system of
partial differential equations from a known conservation law and admitted symmetries. The …

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 …

The paper deals with non-linear Klein–Gordon type equations c (x) utt=[a (x) f (u) ux] x+ b (x)
g (u). The direct method for constructing functional separable solutions in implicit form to non …

In this paper, we concentrate on the Lie symmetry structure of a system of multi-dimensional
time-fractional partial differential equations (PDEs). Specifically, we first give an explicit …