The main attention of this study is focused on the interaction dynamics of breather, and
hybrid solitons and breather for an extended generalization of Vakhnenko equation. The …

We report a novel type of breather by studying the Vakhnenko equation (VE) describing high-
frequency wave (HFW) propagation in electromagnetic physics. By extending the bilinear …

A Bäcklund transformation both in bilinear and in ordinary form for the transformed
generalised Vakhnenko equation (GVE) is derived. It is shown that the equation has an …

An operator T on a Banach space is called 'semi B-Fredholm'if for some n\in {\tf=" times-b" N}
the range R (T\;\!^ n) of T\;\!^ n is closed and the induced operator T_n on R (T\;\!^ n) semi …

The multilinear variable separation approach and the related “universal” formula have been
applied to many (2+ 1)-dimensional nonlinear systems. Starting from the universal formula …

A variety of methods for examining the properties and solutions of nonlinear evolution
equations are explored by using the Vakhnenko equation (VE) as an example. The VE …

In this article, we investigate the dynamical interaction behavior of a short pulse equation in
optical fibers with fast-varying packets. We systematically unearth the interaction dynamics …

We consider a family of non-evolutionary partial differential equations, labelled by a single
parameter b, all of which admit multi-peakon solutions. For the two special integrable cases …

A Bäcklund transformation both in bilinear form and in ordinary form for the transformed
Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse …

Travelling-wave solutions of the Degasperis–Procesi equation are investigated. The
solutions are characterized by two parameters. For propagation in the positive x-direction …