相关论文: Painlev\'e structure of a multi-ion electrodiffusi…
An interpolation problem related to the elliptic Painlev\'e equation is formulated and solved. A simple form of the elliptic Painlev\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also…
Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.
Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.
We find and study a five-parameter family of four-dimensional coupled Painlev\'e V systems with affine Weyl group symmetry of type $D_5^{(1)}$. We then give an explicit description of a confluence from those systems to a four-parameter…
Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…
The paper concerns asymptotic studies for the sixth Painlev\'e transcendent as independent variable tends to infinity. The primary tool is averaging and the Whitham method. Elliptic ansatz, appropriate modulation equation and asymptotics…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation, both allowing for arbitrary dimensionality, and non-linearity. For one of these generalisations, we characterise all solutions…
Quantum fluids of light are photonic counterpart to atomic Bose gases and are attracting increasing interest for probing many-body physics quantum phenomena such as superfluidity. Two different configurations are commonly used: the confined…
The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both…
New manifestly gauge-invariant forms of two-dimensional generalized dispersive long-wave and Nizhnik-Veselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous…
This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two…
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system and obtain higher sharp regularity across the free boundary. Additionally,…
A useful semiclassical method to calculate eigenfunctions of the Schroedinger equation is the mapping to a well-known ordinary differential equation, as for example Airy's equation. In this paper we generalize the mapping procedure to the…
The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink…
The Painlev\'e analysis of a generic multiparameter N=2 extension of the Korteweg-de Vries equation is presented. Unusual aspects of the analysis, pertaining to the presence of two fermionic fields, are emphasized. For the general class of…
n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing…
Novel sequences of approximants to solutions of Painlev\'e II on finite intervals of the real line, with Neumann boundary conditions, are constructed. Numerical experiments strongly suggest convergence of these sequences in a surprisingly…
We utilise a recent approach via the so-called re-scaling method to derive a unified and comprehensive theory of the solutions to Painleve's differential equations (I), (II) and (IV), with emphasis on the most elaborate equation (IV).
Petrovskii elliptic systems of linear differential equations given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the…