We present a review of results of the so-called Painlevé singularity approach to the
investigation of the integrability of dynamical systems with finite and infinite number of …

Nonlinear Schrödinger's equation and its variation structures assume a significant job in
soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with …

A generalized method, which is called the generally projective Riccati equation method, is
presented to find more exact solutions of nonlinear differential equations based upon a …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

Under the travelling wave transformation, Calogero–Degasperis–Focas equation is reduced
to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is …

The characteristic feature of the so‐called Painlevé test for integrability of an ordinary (or
partial) analytic differential equation, as usually carried out, is to determine whether all its …

Lie systems form a class of systems of first-order ordinary differential equations whose
general solutions can be described in terms of certain finite families of particular solutions …

Applying the improved generalized method, which is a direct and unified algebraic method
for constructing multiple travelling wave solutions of nonlinear partial differential equations …

In this paper, first, the general projective Riccati equation method (PREM) is applied to
derive variable separation solutions of (2+ 1)-dimensional systems. By further studying, we …

In this paper, with the help of symbolic computation, the projective Riccati equations method
is extended to find some new exact solutions of the nonlinear Schrödinger model with …