For an arbitrary perturbation operator, equations for the modulation of the parameters of the
KdV soliton are obtained. The asymptotic behavior of the first correction is investigated, and …

In order to investigate corrections to the common KdV approximation for surface water
waves in a canal, we derive modulation equations for the evolution of long wavelength initial …

The interaction of two higher-order solitary waves, governed by the extended Korteweg–de
Vries (KdV) equation, is examined. A nonlocal transformation is used on the extended KdV …

In order to investigate corrections to the common KdV approximation to long waves, we
derive modulation equations for the evolution of long wavelength initial data for a …

Results of fully nonlinear numerical simulations of the interaction of two mode‐1 solitary
internal waves, both propagating in the same direction, are presented. After the interaction …

Solitary wave interaction is examined, for the case of surface waves on shallow water, by
using an extended Benjamin–Bona–Mahony (eBBM) equation. This equation includes …

The paper studies the influence of the time discretizations when simulating some
phenomena involving more than one solitary wave. Taking the KdV equation as a case …

We propose a new way to handle obstacles to asymptotic integrability in perturbed nonlinear
PDEs in the method of normal forms (NFs) in the case of multiwave solutions. Instead of …

Для интегро-дифференциального уравнения с быстро осциллирующим ядром типа
Коши доказана разрешимость и равномерная по малому параметру е ог раниченность …

The small-amplitude, long-wavelength perturbation expansion of the water-wave equation
has been extended to the fourth order of approximation for overtaking collisions of solitary …