On some configurations of oppositely charged trapped vortices in the plane

DOI10.1016/j.aam.2020.102099zbMath1461.81147arXiv1810.11529OpenAlexW3112361502WikidataQ115996913 ScholiaQ115996913MaRDI QIDQ2221790

Panayotis G. Kevrekidis, Heather A. Harrington, Jonathan D. Hauenstein, Paolo Tripoli, Emilie Dufresne

Publication date: 2 February 2021

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.11529

zbMATH Keywords

Bose-Einstein condensatesinvariant theorystanding wave vortex configurations in planesymbolic computational methods

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Wave equation (35L05) Statistical mechanics of liquids (82D15) Vortex methods applied to problems in fluid mechanics (76M23) Bosonic systems in quantum theory (81V73)

Uses Software

• Macaulay2
• Magma
• Maple
• Mathematica
• SINGULAR
• Bertini

Cites Work

• Groebner basis methods for stationary solutions of a low-dimensional model for a shear flow
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• The complexity of the word problems for commutative semigroups and polynomial ideals
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• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Few-particle vortex cluster equilibria in Bose–Einstein condensates: existence and stability
• A Hilbert Scheme in Computer Vision
• Application of Groebner Basis Methodology to Nonlinear Mechanics Problems
• Regeneration homotopies for solving systems of polynomials
• Computer Algebra in Systems Biology
• The Defocusing Nonlinear Schrödinger Equation
• Vortices and polynomials
• Multi-vortex crystal lattices in Bose–Einstein condensates with a rotating trap
• Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of N vortices in the plane
• Ideals, Varieties, and Algorithms
• Generating functions, polynomials and vortices with alternating signs in Bose–Einstein condensates
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Algorithms in invariant theory
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