Related papers: The scattering approach for the Camassa-Holm equat…
A simple algorithm for the inverse scattering approach to the Camassa-Holm equation is presented.
The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this letter we deal with such a two-component integrable system of coupled…
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the…
We study the stochastic Camassa-Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave solution of the unperturbed equation, the solution decomposes into the sum of a randomly modulated…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
We establish the inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data. In particular, it is employed to prove existence of weak solutions for the corresponding Cauchy problem.
We present two initial profiles to the Camassa-Holm equation which yield solutions with accumulating breaking times.
We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.
General equations for the calculation of amplitudes are presented. As an illustration of application of proposed formulae we calculate electron-electron scattering amplitudes.
The Cauchy problem for the Camassa -- Holm equation with step-like initial conditions is reformulated as a Riemann -- Hilbert problem. The the initial value problem solution is obtained then in a parametric form from the Riemann -- Hilbert…
This paper examines a generalization of the Camassa-Holm equation from the perspective of integrability. Using the framework developed by Dubrovin on bi-Hamiltonian deformations and the general theory of quasi-integrability, we demonstrate…
We study the scattering problems for the quadratic Klein-Gordon equations with radial initial data in the energy space. For 3D, we prove small data scattering, and for 4D, we prove large data scattering with mass below the ground state.
In this article we numerically revisit the long-time solution behavior of the Camassa-Holm equation. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.
Considered in this paper is the modified Camassa-Holm equation with cubic nonlinearity, which is integrable and admits the single peaked solitons and multi-peakon solutions. The short-wave limit of this equation is known as the short-pulse…
In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.