Interacting helical traveling waves for the Gross-Pitaevskii equation

DOI10.4171/AIHPC/32MaRDI QIDQ2693538

Juan Dávila, Rémy Rodiac, Manuel A. del Pino, María Medina

Publication date: 21 March 2023

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.10718

zbMATH Keywords

Gross-Pitaevskii equationhelicestraveling waves equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Traveling wave solutions (35C07) Ginzburg-Landau equations (35Q56) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Smooth branch of rarefaction pulses for the nonlinear Schrödinger equation and the Euler-Korteweg system in 2d

Cites Work

• Vortex rings for the Gross-Pitaevskii equation in \(\mathbb R^3\)
• On the motion of a curve by its binormal curvature
• The Cauchy problem for the Gross--Pitaevskii equation
• Variational reduction for Ginzburg-Landau vortices
• Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\)
• Vortex rings for the Gross-Pitaevskii equation
• Leapfrogging vortex rings for the three dimensional Gross-Pitaevskii equation
• Nearly parallel vortex filaments in the 3D Ginzburg-Landau equations
• Travelling waves for the Gross-Pitaevskii equation in dimension larger than two
• A qualitative study of the real solutions of an ordinary differential equation related to the Ginzburg-Landau equation
• Dynamics of nearly parallel vortex filaments for the Gross-Pitaevskii equation
• Interacting helical vortex filaments in the three-dimensional Ginzburg-Landau equation
• Travelling helices and the vortex filament conjecture in the incompressible Euler equations
• Two remarks on solutions of Gross-Pitaevskii equations on Zhidkov spaces
• Schrödinger group on Zhidkov spaces
• Travelling waves for the Gross-Pitaevskii equation. II
• On the interaction of nearly parallel vortex filaments
• Vortex helices for the Gross-Pitaevskii equation
• Coercivity for travelling waves in the Gross-Pitaevskii equation in \(\mathbb{R}^2\) for small speed
• Traveling vortex helices for Schrödinger map equations
• Traveling wave solutions of the Schrödinger map equation
• The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity
• Locally minimising solutions of − Δu = u(1 − |u|²) in R²
• Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation
• Simplified equations for the interaction of nearly parallel vortex filaments
• Vortex Ring Pinning for the Gross--Pitaevskii Equation in Three-Dimensional Space
• Smooth branch of travelling waves for the Gross-Pitaevskii equation in R2 for small speed
• Multivortex Traveling Waves for the Gross--Pitaevskii Equation and the Adler--Moser Polynomials
• Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime
• Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity
• Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity
• Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
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