This survey article reviews the theory and application of homoclinic orbits to equilibria in
reversible continuous-time dynamical systems, where the homoclinic orbit and the …

This paper surveys the classification of integrable evolution equations whose field variables
take values in an associative algebra, which includes matrix, Clifford, and group algebra …

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 …

The tanh-function method for finding explicit travelling solitary wave solutions to non-linear
evolution equations is described. The method is usually extremely tedious to use by hand …

In this work we investigate two extended (3+ 1)-dimensional Jimbo–Miwa equations. We use
the simplified Hirota's method to derive multiple soliton solutions of distinct physical …

The study of spatial patterns in extended systems, and their evolution with time, poses
challenging questions for physicists and mathematicians alike. Waves on water, pulses in …

This paper considers an unfolding of a degenerate reversible 1–1 resonance (or
Hamiltonian–Hopf) bifurcation for four-dimensional systems of time reversible ordinary …

Relaxing the distinguished ordering underlying the derivation of soliton supporting
equations leads to new equations endowed with nonlinear dispersion crucial for the …

This book provides a self-contained presentation of classical and new methods for studying
wave phenomena that are related to the existence and stability of solitary and periodic …

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 …