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Padé approximants are used to find approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for a uniform condensate and condensates with axisymmetric trapping potentials. Rational function and generalised rational function approximations of axisymmetric solitary waves of the Gross-Pitaevskii equation are obtained in… (More)

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to… (More)

The singular manifold method and partial fraction decomposition allow one to find some special solutions of nonintegrable partial differential equations Ž. PDE in the form of solitary waves, traveling wave fronts, and periodic pulse trains. The truncated Painleve expansion is used to reduce a nonlinear´PDE to a multilinear form. Some special solutions of… (More)

The Bose condensate model is used to analyse the superfluid flow around an ion (modelled as a solid sphere) and to elucidate the mechanism of vortex ring emission from the sphere that occurs if its velocity exceeds a critical value. An asymptotic expansion is developed for the steady subcritical flow, using the ratio of the healing length to the radius of… (More)

The first genetic maps were constructed by linkage analysis. Physical mapping techniques, such as radiation hybrids and complete sequencing, produce a different picture. For the purposes of population genetics, clinical genetics, and genetic epidemiology, it is important to harmonize and amalgamate existing genetic and physical maps. Among other things,… (More)

The results of theoretical and numerical studies of the Gross-Pitaevskii (GP) model are reviewed. This model is used to elucidate different aspects of superfluid behaviour: the motion, interactions, annihilations, nucleation and reconnections of vortex lines, vortex rings, and vortex loops; the motion of impurities; flow through apertures; superfluid… (More)

A gas of magnons in magnetic films differs from all other known systems demonstrating Bose-Einstein condensation (BEC), since it possesses two energetically degenerate lowest-energy quantum states with non-zero wave vectors ±k(BEC). Therefore, BEC in this system results in a spontaneously formed two-component Bose-Einstein condensate described by a linear… (More)

The Gross-Pitaevskii (GP) equation admits a two-dimensional solitary wave solution representing two mutually self-propelled, anti-parallel straight line vortices. The complete sequence of such solitary wave solutions has been computed by Jones and Roberts (J. Phys. A, 15, 2599, 1982). These solutions are unstable with respect to three-dimensional… (More)

The Bose condensate model is used to elucidate the motion of the electron bubble in superfluids. An asymptotic expansion is developed for steady subcritical flow. Numerical integration of the coupled nonlinear Schrödinger equations, that describe the evolution of the wavefunctions of the Bose condensate and the impurity, is used to study the nucleation and… (More)

The nonlinear Schrödinger equation is used to analyze the superfluid flow around an ion and to elucidate the vortex nucleation process. Asymptotic expansion for the flow is used to find the critical velocity of the ion for vortex production. 3D numerical calculations demonstrate, that if the axisymmetry of the flow is broken by introducing a solid boundary… (More)