An inverse scattering method is developed for the Camassa–Holm equation. As an
illustration of our approach the solutions corresponding to the reflectionless potentials are …

An explicit reciprocal transformation between a two-component generalization of the
Camassa–Holm equation, called the 2-CH system, and the first negative flow of the AKNS …

The multisoliton solutions of the Degasperis–Procesi (DP) equation are constructed by
means of a reduction procedure (CKP reduction) for the multisoliton solutions of the …

A generalization of integrable peakon equations with cubic nonlinearity and the Degasperis–
Procesi equation with peakon solutions is proposed, which is associated with a 3× 3 matrix …

Based on a multidimensional Riemann theta function, the Hirota bilinear method is extended
to explicitly construct multiperiodic (quasiperiodic) wave solutions for the (2+ 1)-dimensional …

Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a
perturbative asymptotic expansion of Euler's equations is considered (to a certain order of …

In this paper, we develop, analyze, and test a local discontinuous Galerkin (LDG) method for
solving the Camassa–Holm equation which contains nonlinear high-order derivatives. The …

With the aid of symbolic computation, a generalized auxiliary equation method is proposed
to construct more general exact solutions to two types of NLPDEs. First, we present new …

A three-component generalization of Camassa–Holm equation with peakon solutions is
proposed, which is associated with a 3× 3 matrix spectral problem with three potentials. With …

In this paper, we propose a new approach to calculate multi-soliton solutions of Camassa-
Holm (CH) equation and modified Camassa-Holm (MCH) equation with the aid of Darboux …