Boltzmann and Vlasov equations played a great role in the past and still play an important
role in modern natural sciences, technique and even philosophy of science. Classical …

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 …

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 …

We present an inverse scattering approach for computing n-peakon solutions of the
Degasperis–Procesi equation (a modification of the Camassa–Holm (CH) shallow water …

We investigate well-posedness in classes of discontinuous functions for the nonlinear and
third order dispersive Degasperis–Procesi equationThis equation can be regarded as a …

We develop the inverse scattering transform (IST) method for the Degasperis–Procesi
equation. The spectral problem is an Zakharov–Shabat problem with constant boundary …

We consider a generalization of the Camassa–Holm (CH) equation with two dependent
variables, called CH2, introduced in a paper by Liu and Zhang (Liu SQ and Zhang Y 2005 J …

We consider a family of non-evolutionary partial differential equations, labelled by a single
parameter b, all of which admit multi-peakon solutions. For the two special integrable cases …

We use an inverse scattering approach to study multipeakon solutions of the Degasperis-
Procesi (DP) equation, an integrable PDE similar to the Camassa-Holm (CH) shallow water …

In the paper we first establish the local well-posedness for a family of nonlinear dispersive
equations, the so called b-equation. Then we describe the precise blow-up scenario …