相关论文: Painlev\'e structure of a multi-ion electrodiffusi…

The non-uniform (or inhomogeneous) electron gas has received much attention in many-body quantum mechanics and quantum chemistry in the early days of density functional theory, mainly as a theoretical device to construct gradient…

A new set of nonlinear coupled equations is derived in the context of small amplitude limit of the general wave equations in a fluid type warm electrons/cold ions plasma irradiated by a continuous laser beam. This limit is proved to be…

A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…

We employ the Sagdeev pseudo-potential method to investigate the propagation of nonlinear ion waves in a relativistically degenerate electron-ion plasmas. The matching criteria for existence of such nonlinear excitations are numerically…

In previous work, Bender and Komijani (2015 \textit{J. Phys. A: Math. Theor.} 48, 475202) studied the first Painlev\'e (PI) equation and showed that the sequence of initial conditions giving rise to separatrix solutions could be…

In this paper, the Painlev\'e property to fractional differential equations (FDEs) are extended and the existence and uniqueness theorems for both linear and nonlinear FDEs are established. The results contribute to the research of…

Nonlinear diffusion equations of spectral transfer are systematically derived for anisotropic magnetohydrodynamics in the regime of wave turbulence. The background of the analysis is the asymptotic Alfv\'en wave turbulence equations from…

Special polynomials associated with rational solutions of the second Painlev\'{e} equation and other members of its hierarchy are discussed. New approach, which allows one to construct each polynomial is presented. The structure of the…

In a counter-ion only charged fluid, Coulomb coupling is quantified by a single dimensionless parameter. Yet, the theoretical treatment of moderately to strongly coupled charged fluids is a difficult task, central to the understanding of a…

A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…

We investigate a system of dense polyelectrolytes in solution. The Langevin dynamics of the system with linearized hydrodynamics is formulated in the functional integral formalism and a transformation made to collective coordinates. Within…

Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…

The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with a tri-diagonal Toeplitz matrix of diffusion coefficients and prove the global existence of solutions using Lyapunov…

This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…

We apply the Painleve test for integrability to a new discrete (differential-difference) nonlinear Schrodinger equation introduced by Leon and Manna. Since the singular expansions of solutions of this equation turn out to contain…

First, starting from two hierarchies of autonomous St\"{a}ckel ODE's, we reconstruct the hierarchy of KdV stationary systems. Next, we deform considered autonomous St\"{a}ckel systems to non-autonomous Painlev\'{e} hierarchies of ODE's.…

The consistent description of kinetic and hydrodynamic processes is applied to the study of ion transport processes in the ionic solution-porous medium system. A system of equations is obtained for the nonequilibrium single-ion distribution…

In this work we study the integrability of a family of nonlinear oscillators. Dynamical systems from this family appear in different applications from mechanics to chemistry. We propose an approach for finding first integrals and…

Eigenvalue problems for linear differential equations, such as time-independent Schr\"odinger equations, can be generalized to eigenvalue problems for nonlinear differential equations. In the nonlinear context a separatrix plays the role of…

We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…