Related papers: Soliton formulation by Moyal algebra
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the…
We prove the orbital stability of soliton solutions for 2D Maxwell--Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle. We reduce the corresponding Hamilton system by…
In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…
In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schr\"odinger equation near anti-continuous limit. Our novel insight is that the analysis of linearized operator, usually…
The concept of integrable boundary value problems for soliton equations on $\mathbb{R}$ and $\mathbb{R}_+$ is extended to bounded regions enclosed by smooth curves. Classes of integrable boundary conditions on a circle for the Toda lattice…
We derive the leading order radiation through tunneling of an oscillating soliton in a well. We use the hydrodynamic formulation with a rigorous control of the errors for finite times.
We have derived the hierarchy of soliton equations associated with the untwisted affine Kac-Moody algebra D^(1)_4 by calculating the corresponding recursion operators. The Hamiltonian formulation of the equations from the hierarchy is also…
Some aspects of the multidimensional soliton geometry are considered.
We present a simple formula for all the conserved charges of soliton theories, evaluated on the solutions belonging to the orbit of the vacuum under the group of dressing transformations. For pedagogical reasons we perform the explicit…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
This work reports on calculations of the deformation energy of a nucleus plus an emitted cluster as a soliton moving on its surface. The potential barrier against the emission of a soliton is calculated within the macroscopic-microscopic…
We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The…
We consider 2D Maxwell-Lorentz equations with extended charged rotating particle. The system admits solitons which are solutions corresponding to a particle moving with a constant velocity and rotating with a constant angular velocity. Our…
Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete…
A classical Calogero model in an external harmonic potential is known to be integrable for any number of particles. We consider here reductions which play a role of "soliton" solutions of the model. We obtain these solutions both for the…
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.