Related papers: Discretization of Camassa-Holm peakon equation usi…
We consider a nonholonomic system describing a rolling of a dynamically non-symmetric sphere over a fixed sphere without slipping. The system generalizes the classical nonholonomic Chaplygin sphere problem and it is shown to be integrable…
The Degasperis-Procesi equation is an approximating model of shallow-water wave propagating mainly in one direction to the Euler equations. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional…
We introduce an integrable time-discretized version of the classical Calogero-Moser model, which goes to the original model in a continuum limit. This discrete model is obtained from pole solutions of a discretized version of the…
We propose new type of discrete and ultradiscrete soliton equations, which admit extended soliton solution called periodic phase soliton solution. The discrete equation is derived from the discrete DKP equation and the ultradiscrete one is…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
We consider the problem of soliton-mean field interaction for the class of asymptotically integrable equations, where the notion of the asymptotic integrability means that the Hamilton equations for the high-frequency wave packet's…
We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves…
In this article, a modification of the rapidly convergent approximation method is proposed to solve a coupled Korteweg-de Vries equations with conformable derivative that govern shallow-water waves. Based on the Leibniz and chain rule of…
We study compact polyhedral surfaces as Riemann surfaces and their discrete counterparts obtained through quadrilateral cellular decompositions and a linear discretization of the Cauchy-Riemann equation. By ensuring uniformly bounded…
Multipeakons are special solutions to the Camassa-Holm equation described by an integrable geodesic flow on a Riemannian manifold. We present a bi-Hamiltonian formulation of the system explicitly and write down formulae for the associated…
A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(n)=so(n)\ltimes\mathbb R^n$. We give a Lagrangian derivation of the…
A non-local evolution equation of the Camassa-Holm type with dissipation is considered. The local well-posedness of the solutions of the Cauchy problem involving the equation is established via Kato's approach and the wave breaking scenario…
The quasipolynomial (QP) generalization of Lotka-Volterra discrete-time systems is considered. Use of the QP formalism is made for the investigation of various global dynamical properties of QP discrete-time systems including permanence,…
The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa-Holm equation. In this paper, we…
In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where…
We establish the asymptotic stability of smooth solitons and multi-solitons for the Camassa-Holm (CH) equation in the energy space $H^1(\R)$. We show that solutions initially close to a soliton converge, up to translation, weakly in…
Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear and its coefficients are piecewise constant. We introduce a…
We extend the Euler-Bernoulli beam problem, formulated as a matrix string equation with a matrix-valued density, to a setting where the density takes values in a Clifford algebra, and we analyze its isospectral deformations. For discrete…
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time…
The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…