Related papers: A complexity approach to the soliton resolution co…
Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear…
Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
Cosmological perturbations with wavelengths smaller than Hubble radius can be handled in the context of Newtonian theory with very high accuracy. The application of this Newtonian approximation, however, is restricted to nonrelativistic…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
The non-topological, stationary and propagating, soliton solutions of the classical continuous Heisenberg ferromagnet equation are investigated. A general, rigorous formulation of the Inverse Scattering Transform for this equation is…
This is a survey article dedicated mostly to the theory of real regular "finite-gap" (algebro-geometrical) periodic and quasiperiodic Sine-Gordon solutions. Long period this theory remained unfinished and ineffective, and by that reason…
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This…
Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen…
In this investigation the light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. It is found that the light trajectory depends on the…
Novel soliton structures are constructed for the Fokas-Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales perturbation theory is used to reduce the equation to a Korteweg-de Vries system…
Although its practical efficiency is unquestionable, it is well known that thermodynamics presents conceptual difficulties from the theoretical point of view. It is shown that the problem comes from an imperfect compatibility between the…
We analyze soliton solutions in the duality-based matrix model. There are two types of solution, a one soliton-antisoliton solution (with the constant boundary condition at infinity) and a periodic solution with an infinite number of…
Nonlinear field model of extremal space-time film is considered. Its space-localized solution in toroidal coordinates with periodic dependence in time is investigated. A field configuration having a form of the twisted lightlike soliton…
The partition function of two-dimensional solitons in a heat bath of mesons is worked out to one-loop. For temperatures large compared to the meson mass, the free energy is dominated by the meson-soliton bound states and the zero modes, a…
In this work we consider the focusing, energy-critical wave equation in 3D radial case. It has been verified that any global or type II blow-up solution decomposes into a superposition of several decoupled grounds states, a free wave and a…
We investigate the descriptive set-theoretic complexity of the solvability of a Borel family of linear equations over a finite field. Answering a question of Thornton, we show that this problem is already hard, namely $\Sigma^1_2$-complete.…
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…
We show that the holographic Complexity = Volume proposal satisfies a very general notion of Momentum/Complexity correspondence (PC), based on the Momentum Constraint of General Relativity. It relates the rate of complexity variation with…
We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of…