相关论文: Poles of Integrale Tritronquee and Anharmonic Osci…

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb-like potentials) and compare their spectra and the sets of eigenfunctions. We…

This paper is a continuation of our analysis, begun in arXiv:1310.2276, of the rational solutions of the inhomogeneous Painleve-II equation and associated rational solutions of the homogeneous coupled Painleve-II system in the limit of…

The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the…

As it has been proven, the determination of general one-dimensional Schr\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\'e IV equation. In this work, it will be shown that some specific…

A starting point of this paper is a classification of quadratic polynomial transformations of the monodromy manifold for the 2x2 isomonodromic Fuchsian systems associated to the Painleve VI equation. Up to birational automorphisms of the…

We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak…

The present paper sketches a framework for solving the wave and Fokker-Planck equations in the ion cyclotron resonance frequency domain fully selfconsistently. It illustrates this can be done by first constructing "building blocks" that are…

The exactly solvable Schr\"{o}dinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called…

The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with…

We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…

We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of…

An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order…

In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…

In the Painleve analysis of nonintegrable partial differential equations one obtains differential constraints describing the movable singularity manifold. We show, for a class of n-dimensional wave equations, that these constraints have a…

We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the $\mathbf{U}(1)$-invariant Klein--Gordon equation in one spatial dimension coupled to an anharmonic oscillator. We also give the complete…

We consider a set of interwoven harmonic oscillators where the acceleration of a given oscillator is determined by the position of its nearest neighbor. We show that this problem of N non-local oscillators with periodic boundary conditions…

The relation between the Painleve equations and the algebraic equations with the catastrophe theory point of view are considered. The asymptotic solutions with respect to the small parameter of the Painleve equations different types are…

Using Painleve singularity structure analysis, we show that coupled higher-order nonlinear Schrodinger (CHNLS) equations admit Painleve property. Using the results of Painleve analysis, we succeed in Hirota bilinearizing the CHNLS…

In this paper we consider a non-linear Schroedinger equation with a cubic nonlinearity and a multi-dimensional double well potential. In the semiclassical limit the problem of the existence of stationary solutions simply reduces to the…