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 …

In this paper we consider a five-parameter equation including the Camassa-Holm and the
Dullin-Gottwald-Holm equations, among others. We prove the existence and uniqueness of …

This work presents an Ovsyannikov type theorem for an autonomous abstract Cauchy
problem in a scale of decreasing Banach spaces, which in addition to existence and …

We study a two-component Novikov system, which is integrable and can be viewed as a two-
component generalization of the Novikov equation with cubic nonlinearity. The primary goal …

In this paper, we consider the Cauchy problem for a two-component peakon system with
cubic nonlinearity, which is a natural multi-component extension of the single Camassa …

This article is concerned with the spectral problem {d ϕ 1 (x)= ϕ 2 (x) dh (x), d ϕ 2 (x)= ϕ 3
(x) dg (x), d ϕ 3 (x)=− λ ϕ 1 (x) dx, x∈(− 1, 1), ϕ 2 (− 1)= 0, ϕ 3 (− 1)= 0, ϕ 3 (1)= 0, which is …

We present a reciprocal transformation which links the Geng-Xue equation to a particular
reduction of the first negative flow of the Boussinesq hierarchy. We discuss two reductions of …

The aim of the present article is to derive explicit formulas for arbitrary non-overlapping pure
peakon solutions of the Geng–Xue (GX) equation, a two-component generalization of …

Considered herein is a two‐component Novikov equations (called Geng‐Xue system for
short) with cubic nonlinearities. The persistence properties and some unique continuation …

In this paper, we study the existence of global conservative solutions to a two-component
Novikov system. The system is an integrable multi-component extension of the Novikov …