相关论文: Deformed multi-variable Fokker-Planck equations

We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the dependence of the coefficients is nonlinear and nonlocal in time with respect to the unknowns. We extend the numerical scheme proposed and studied recently by the…

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of…

We present a priori estimates and unique solvability results in the mixed-norm Lebesgue spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equation in divergence form. The leading coefficients are bounded uniformly nondegenerate with respect…

The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincare group in 1+1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a…

We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi…

The Fokker-Planck (FP) particle method accelerates rarefied-gas simulations by replacing the binary collisions of the commonly used Direct Simulation Monte Carlo (DSMC) method with a drift=diffusion process. Like all particle methods, the…

We consider exact and quasi-exact solvability of the one-dimensional Fokker-Planck equation based on the connection between the Fokker-Planck equation and the Schr\"odinger equation. A unified consideration of these two types of solvability…

After a short outline of the factorization and Grassmann picture of the one-dimensional (1D) Fokker-Planck (FP) equation, we consider a class of spatially-inhomogeneous solutions of the 2D FP equation with symmetric 2D (super)potentials. We…

We introduce a stochastic particle system that corresponds to the Fokker-Planck equation with decay in the many-particles limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an…

We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which is an sl(M+1) module, and we thus call it type A'. We…

The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the $n$-soliton solutions of the mKdV…

The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…

We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…

Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schr\"odinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential…

Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical…

This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…

An $L^2(R^d)$-valued stochastic N-interacting particle systems is investigated. Existence and uniqueness of solutions for the degenerate nonlinear Fokker-Planck equation for probability measures that corresponds to the mean field limit…

We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…

The known prepotential solutions F to the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation are parametrized by a set {alpha} of covectors. This set may be taken to be indecomposable, since F_{alpha oplus beta}=F_{alpha}+F_{beta}. We…

Recently, Feh\'er and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars-Schneider $n$-particle systems, with phase space symplectomorphic to the $(n-1)$-dimensional complex projective space.…