Related papers: On a Camassa-Holm type equation with two dependent…
We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between…
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…
The theory of Poisson-Lie groups and Lie bialgebras plays a major role in the study of one dimensional integrable systems; many families of integrable systems can be recovered from a Lax pair which is constructed from a Lie bialgebra…
We study MNLS related to the D.III-type symmetric spaces. Applying to them Mikhailov reduction groups of the type $\mathbb{Z}_r\times \mathbb{Z}_2$ we derive new types of 2-component NLS equations. These are {\bf not} counterexamples to the…
In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schr\"odinger equation, the complex…
We prove existence of a global conservative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line, allowing for nonvanishing and distinct asymptotics at plus and minus infinity. The solution is proven to…
We construct a global continuous semigroup of weak periodic conservative solutions to the two-component Camassa-Holm system, $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}+\eta\rho\rho_x=0$ and $\rho_t+(u\rho)_x=0$, for initial data…
For a 2-component Camassa-Holm equation, as well as a 2-component generalization of the modified Camassa-Holm equation, nonlocal infinitesimal symmetries quadratically depending on eigenfunctions of linear spectral problems are constructed…
We propose an extension of the Dubrovin-Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few corrections leads to the conjecture that…
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems…
Motivated by the paper (Beals, Sattinger and Szmigielski, Adv. Math. 154 (2000) 229--257), we propose an extension of the Camassa-Holm equation, which also admits the multipeakon solutions. The novel aspect is that our approach is mainly…
A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by…
In this paper, we consider a generalized two component Camassa-Holm system. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly…
In this paper, we analyze a substructuring type algorithm for the Cahn-Hilliard (CH) equation. Being a nonlinear equation, it is of great importance to develop efficient numerical schemes for investigating the solution behaviour of the CH…
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS). CSS is $L^{2}$-critical, admits solitons, and has the pseudoconformal symmetry. In this work, we consider pseudoconformal blow-up solutions under $m$-equivariance,…
In this paper, we study the global well-posedness for the Camassa-Holm(C-H) equation with a forcing in $H^1(\mathbb{R})$ by the characteristic method. Due to the forcing, many important properties to study the well posedness of weak…
A nonlinear coupled Choi-Camassa model describing one-dimensional incompressible motion of two non-mixing fluid layers in a horizontal channel has been derived in Ref.1. An equivalence transformation is presented, leading to a special…
In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian…
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $\alpha^k$-derivations and provide a classification in low dimension. We…
We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…