This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent, well-pose...

We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta time. apply this to create new classes of fully-discrete several nonlinear dispersive wave equations: Benjamin-Bona-Mahony (BBM), Fornberg-Whitham, Camassa-Holm, Degasperis-Procesi, Holm-Hone, the BBM-BBM system. These f...

In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves discontinuous first-order derivative at wave peak. this paper, we apply multi-layer physics-informed neural networks (PINNs) deep learning to successfully study data-driven and periodic solutions some well-known dispersion initial-boundary ...

Peakons and periodic peakons are two kinds of special symmetric traveling wave solutions, which have important applications in physics, optical fiber communication, other fields. In this paper, we study the orbital stability for a generalized Camassa–Holm equation with quadratic cubic nonlinearities (mCH–Novikov–CH equation). It is generalization some classical equations, such as (CH) equation,...