Padé approximations of solitary wave solutions of the Gross–Pitaevskii equation

2003/06/30 by Natalia G. Berloff · 2 citations
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Context (archaeology) #Gross–Pitaevskii equation #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Padé approximant #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Rational function #Rotational symmetry #Strong Light-Matter Interactions #Vortex #cond-mat.soft

paper · pdf · doi:10.1088/0305-4470/37/5/011

In press by Journal of Physics: Mathematics and General

arxiv created 2003/12/19 · openalex publication_date 2004/01/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Pade ́ 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 generalized rational function approximations of axisymmetric solitary waves of the Gross–Pitaevskii equation are obtained in two and three dimensions. These approximations are used to establish a new mechanism of vortex nucleation as a result of solitary wave interactions. PACS numbers: 03.75.Lm, 47.37.+q, 67.40.Vs 1.

Citations

• Analytical Solution for Nonlinear Schrödinger Vortex Reconnection
• Evolution of rarefaction pulses into vortex rings
• Coherent Dynamics of Vortex Formation in Trapped Bose-Einstein Condensates
• Motions in a Bose condensate: VII. Boundary-layer separation

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