Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

Peaked periodic waves in the Camassa--Holm equation are revisited. Linearized evolution
equations are derived for perturbations to the peaked periodic waves, and linearized …

This paper is concerned with two classes of cubic quasilinear equations, which can be
derived as asymptotic models from shallow-water approximation to the 2D incompressible …

We study the orbital stability of smooth solitary wave solutions of the Novikov equation,
which is a Camassa–Holm-type equation with cubic nonlinearities. These solitary waves are …

We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa–
Holm equations. The smooth solitary waves exist on the constant background. In the …

The Novikov equation is a peakon equation with cubic nonlinearity, which, like the Camassa–
Holm and the Degasperis–Procesi, is completely integrable. In this paper, we study the …

In the present work we revisit the b-family model of peakon equations, containing as special
cases the b= 2 (Camassa–Holm) and b= 3 (Degasperis–Procesi) integrable examples. We …

Consideration herein is a big class of nonlocal partial differential equations including some
classical shallow water models such as b-family equation, Novikov equation, rotation …

In this paper, we propose a local discontinuous Galerkin (LDG) method for the Novikov
equation that contains cubic nonlinear high-order derivatives. Flux correction techniques are …

We prove that the two-component peakon solutions are orbitally stable in the energy space.
The system concerned here is a two-component Novikov system, which is an integrable …