Related papers: Multipeakons and the Classical Moment Problem
In the standard theory of delay equations, the fundamental solution does not 'live' in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators…
An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system…
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 a previous work, the author and D.C. Dobson proposed a numerical method for solving the complex Helmholtz equation based on the minimization variational principles developed by Milton, Seppecher, and Bouchitte. This method results in a…
In this paper, we study the Cauchy problem of a higher-order $\mu$-Camassa-Holm equation. We first establish the Green's function of $(\mu-\partial_{x}^{2}+\partial_{x}^{4})^{-1}$ and local well-posedness for the equation in Sobolev spaces…
Full indefinite Stieltjes moment problem is studied via the step-by-step Schur algorithm. Naturally associated with indefinite Stieltjes moment problem are generalized Stieltjes continued fraction and a system of difference equations,…
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…
In this paper, an approach is developed to solve the three body problem involving masses which posses spherical symmetry. The problem dates back to the times of Poincare, and is undoubtedly one of the oldest of unsolved problems of…
In this paper, we prove that the existence and uniqueness of globally weak solutions to the Cauchy problem for the weakly dissipative Camassa-Holm equation in time weighted $H^1$ space. First, we derive an equivalent semi-linear system by…
A dressing method is applied to a matrix Lax pair for the Camassa-Holm equation, thereby allowing for the construction of several global solutions of the system. In particular solutions of system of soliton and cuspon type are constructed…
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or…
In this article, we study the perturbational method to construct the non-radially symmetric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitutional method and the separation method to…
The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Stieltjes moment problems in the most general case. These results are generalizations of results of Chen and Hu [5,17] which…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
We study the long-time asymptotics of solution of the Cauchy problem for the Camassa-Holm equation with a step-like initial datum. By using the nonlinear steepest descent method and the so-called $g$-function approach, we show that the…
Active droplets emit a chemical solute at their surface that modifies their local interfacial tension. They exploit the nonlinear coupling of the convective transport of solute to the resulting Marangoni flows to self-propel. Such swimming…
The head-on collision of two nonrotating axisymmetric equal mass black holes is treated numerically. We take as initial data the single parameter family of time-symmetric solutions discovered by Misner which consists of two Einstein-Rosen…
It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves, which have been not reported for other mainstream models of shallow water waves. In this letter, the closed-form solutions of peaked solitary waves of…
The time dependent Schr\"odinger equation for $\pi^+$--$\pi^-$ pairs, which are emitted from the interaction zone in relativistic nuclear collisions, is solved using wavepacket states. It is shown that the Coulomb enhancement in the…
We consider Hamiltonian functions of classical type, namely even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton's equations such that the generalized momenta are zero on two different…