Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

In this paper, the stochastic Nizhnik-Novikov-Veselov (NNV) system, which is a two-
dimensional with a multiplicative noise in the Ito sense is studied for simple periodic wave …

A direct approach to exact solutions of nonlinear partial differential equations is proposed,
by using rational function transformations. The new method provides a more systematical …

The sn-and cn-function methods for finding nonsingular periodic-wave solutions to nonlinear
evolution equations are described in a form suitable for automation, where sn and cn are the …

Algorithms are presented for the tanh-and sech-methods, which lead to closed-form
solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New …

This paper studies complex solutions and solitons solutions to the Klein-Gordon-Zakharov
equations (KGZEs). Solitons solutions including bright, dark, W-shape bright, breather also …

We extend the definition of the classical Jacobi polynomials withindexes α, β>− 1 to allow α
and/or β to be negative integers. We show that the generalized Jacobi polynomials, with …

Exact solutions to some nonlinear partial differential equations, including (2+ 1)-dimensional
breaking soliton equation, sine-Gordon equation and double sine-Gordon equation, are …

We introduce a family of generalized Jacobi polynomials/functions with indexes α, β∈ R
which are mutually orthogonal with respect to the corresponding Jacobi weights and which …

In this paper, we show out the chirped and the corresponding chirp with their stability to the
perturbed Chen–Lee–Liu equation with self-phase modulation and nonlinear dispersions …