Exact solutions of nonlinear differential equations are of great importance to the theory and
practice of complex systems. The main point of this review article is to discuss a specific …

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 …

Symmetry plays key roles in modern physics especially in the study of integrable systems
because of the existence of infinitely many local and nonlocal generalized symmetries. In …

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 …

By means of a special variable separation approach, a common formula with some arbitrary
functions has been obtained for some suitable physical quantities of various (2+ 1) …

Starting from a known Lax pair, one can get some infinitely many coupled Lax pairs, infinitely
many nonlocal symmetries and infinitely many new integrable models in some different …

Differential equations, especially nonlinear, present the most effective way for describing
complex physical processes. Methods for constructing exact solutions of differential …

We introduce a new class of symmetries, that strictly includes Lie symmetries, for which there
exists an algorithm that lets us reduce the order of an ordinary differential equation. Many of …

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 the authors first present an algorithm for calculating the determining equations
associated with so-called “nonclassical method” of symmetry reductions (à la Bluman and …