Novel travelling wave structures: few-cycle-pulse solitons and soliton molecules

Abstract

We discuss a fifth order KdV (FOKdV) equation via a novel travelling wave method by introducing a background term. Results show that the background term plays an essential role in finding new abundant travelling wave structures, such as the soliton induced by negative background, the periodic travelling wave excited by the positive background, the few-cycle-pulse (FCP) solitons with and without background, the soliton molecules excited by the background. The FCP solitons are first obtained for the FOKdV equation.

Bounded states for breathers–soliton and breathers of sine–Gordon equation

“…The nonzero background term motivates us to search for more meaningful solutions. Recent studies [13], [29] show that some special soliton solutions related to the nonzero background to some nonlinear systems have been found. These soliton solutions, such as few-cyclesoliton solutions first obtained from the travelling wave method are excited by the background.…”