Related papers: Multi-component generalization of Camassa-Holm equ…
In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the…
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 aid of Darboux transformation (DT). The new approach simplifies the approach presented…
The second part of the theory for the multicomponent nonisothermal nucleation is presented. The solution of the kinetic equation already derived in the first part is given with the help of the Chapman-Enskog procedure. At first the…
The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation…
We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized pulses propagate in anisotropic media.
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
In this paper, we study blow-up phenomena for the rotation-two-component Camassa- Holm (R2CH) system, a model of equatorial water waves that includes the effect of the Coriolis force. We first derive the precise blow-up scenario for R2CH…
We propose realizations of the Poisson structures for the Lax representations of three integrable $n$-body peakon equations, Camassa--Holm, Degasperis--Procesi and Novikov. The Poisson structures derived from the integrability structures of…
We describe a class of the singular solutions to the multicomponent analogs of the Lam{\'e} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling…
This paper investigates the Cauchy problem of a generalized Camassa-Holm equation with quadratic and cubic nonlinearities (alias the mCH-Novikov-CH equation), which is a generalization of some special equations such as the Camassa-Holm (CH)…
The squared eigenfunctions of the spectral problem associated with the Camassa-Holm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized…
In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral problems of the tcCH equations with $4\times4$ the Lax pair.…
In this paper, we are concerned with the stability of 2-soliton solutions on a nonzero constant background for the modified Camassa-Holm equation with cubic nonlinearity. By employing conserved quantities in terms of the momentum variable…
We develop a direct method for solving a modified Camassa-Holm equation with cubic nonlinearity and linear dispersion under the rapidly decreasing vanishing boundary condition. We obtain a compact parametric representation for the…
The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian…
We first establish local well-posedness for a periodic 2-component Camassa-Holm equation with vorticity. We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the…
A general family of peakon equations is introduced, involving two arbitrary functions of the wave amplitude and the wave gradient. This family contains all of the known breaking wave equations, including the integrable ones: Camassa-Holm…
In this work, we introduce a new two component fifth-order bi-Hamiltonian sys- tem admitting the scalar Kupershmidt equation as a reduction.
The paper contains the generalization of usual lattice model of multicomponent systems. The generalization is related to account the following factors: 1. The short-range parts of interatomic repulsions. These repulsions are not identical…
A generalization of the negative Camassa-Holm hierarchy to 2+1 dimensions is presented under the name CHH(2+1). Several hodograph transformations are applied in order to transform the hierarchy into a system of coupled CBS…