This paper studies (2+ 1)-dimensional Konopelchenko–Dubrovsky equation and (2+ 1)-
dimensional KdV equation via a modified auxiliary equation technique. These two systems …

This paper investigates the Kadomtsev–Petviashvili I equation, which describes the variation
of shallow-water wave amplitude in the transverse direction, making it applicable to the …

The KdV equation can be derived in the shallow water limit of the Euler equations. Over the
last few decades, this equation has been extended to include higher-order effects. Although …

A weakly nonlinear fully dispersive model equation is derived which describes the
propagation of waves in a thin elastic body overlying an incompressible inviscid fluid. The …

The Whitham equation is a non-local, nonlinear partial differential equation that models the
temporal evolution of spatial profiles of surface displacement of water waves. However …

An extended fifth order Korteweg-de-Vries (efKdV) equation is an important equation in
fluids dynamics for the description of nonlinear wave processes, and contains quite a …

Abstract The Green–Naghdi system is used to model highly nonlinear weakly dispersive
waves propagating at the surface of a shallow layer of a perfect fluid. The system has three …

This article takes into account the Korteweg–de Vries (KdV) equation as an approximate
model of long waves of small amplitude at the free surface with inviscid fluid. It is …

Starting from a non-isospectral problem, we derive a hierarchy of nonlocal vector Gross-
Pitaevskii (NVGP) equations with space-time external potential, which includes the nonlocal …

It is well known that the Korteweg–de Vries (KdV) equation has an infinite set of conserved
quantities. The first three are often considered to represent mass, momentum, and energy …