Soliton molecules can be formed in some possible mechanisms both theoretically and
experimentally. In this paper, we introduce a new mechanism, namely the velocity resonant …

In this letter, we study a (3+ 1)-dimensional nonlinear Geng equation. The Hirota bilinear
method is employed upon this equation, then the one-to four-order solutions are calculated …

We study solitary wave solutions of the fifth-order Korteweg–de Vries equation which
contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional …

Several threads of the last 25 years' developments in nonlinear wave theory that stem from
the classical Korteweg–de Vries (KdV) equation are surveyed. The focus is on various …

Traveling wave solutions have been well studied for various nonlinear systems. However,
for high order nonlinear physical models, there still exist various open problems. Here …

In this paper we examine the effect of delamination on wave scattering, with the aim of
creating a control measure for layered waveguides of various bonding types. Previous works …

Abstract We present new (2+ 1)-dimensional extended KdV (KdV2) equation derived within
an ideal fluid model. Next, we show several families of analytic solutions to this equation …

Soliton molecules may be formed in some possible mechanisms in both theoretical and
experimental aspects. In this letter, we introduce a new possible mechanism, the velocity …

We study the problem of gravity surface waves for an ideal fluid model in the (2+ 1)-
dimensional case. We apply a systematic procedure to derive the Boussinesq equations for …

In this study, bottom topography with small-scale disturbances is incorporated into the first-
order steady Korteweg–de Vries (KdV) type equation to reveal the detailed spatial variations …