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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 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)
Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behavior. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyze the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a(More)
Semiconductor microcavities are used to support freely flowing polariton quantum liquids allowing the direct observation and optical manipulation of macroscopic quantum states. Incoherent optical excitation at a point produces radially expanding condensate clouds within the planar geometry. By using arbitrary configurations of multiple pump spots, we(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)
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)
Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose(More)