A detailed survey of the technique of perturbation theory for nearly integrable systems,
based upon the inverse scattering transform, and a minute account of results obtained by …

The sine-Gordon equation is, arguably, one of the most popular nonlinear wave models.
This feature is due to a number of appealing traits of this system. One such characteristic is …

We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB
system (also called Pedlosky system), which describes the evolution of wave-packets in a …

A formalism for systematically deriving second order accurate finite difference algorithms
which conserve certain invariant quantities in the original nonlinear PDEs is presented …

The Riemann problem of the defocusing AB system is explored by Whitham modulation
theory. As a result, the modulation periodic wave solutions along with the corresponding …

This paper mainly discusses the numerical solution of Sine–Gordon (SG) equation which is
widely used in engineering field. Different from the classical numerical calculation method …

In this article, we present the stability analysis and approximate solutions of circular ring
solitary solitons wave for (2+ 1)-dimensional nonlinear sine-Gordon equation using time …

We review the history of the soliton, since the first recorded observation of the'great solitary
wave'by Russell in 1834, as a means of developing the mathematical properties of a large …

Evolution equations are developed for weakly nonlinear baroclinic wave packets in a flow
with continuous shear and stratification. When wave dispersion is forced by using sloping …

This chapter offers an overview of the vast research area developed around the sine-Gordon
(sG) equation, including solution methods and various nonlinear modes generated by this …