Novel solitary patterns in a class of regularized Gardner equations

Abstract

We introduce and study a class of equations that merge the Gardner’s-type, non-convex, advection with regularized long-wave dispersion, also known as Benjamin–Bona–Mahony equation, to the effect that unlike the unidirectional Gardner solitons, the presented model supports bidirectional propagation of at least three types of solitary waves and begets a whole gallery of chase and collision interactions. Among the novel features of our model, we mention the possibility that one of the solitons reverses its direction upon interaction with another soliton. Extension of the model to higher dimensions typically causes the newly found solitary waves to split into a countable sequence of multi-modal solitary waves wherein either mode’s amplitude increases with its modality, or the modes condense near their potential’s top.