Multiple normalized solutions for two coupled Gross-Pitaevskii equations with attractive interactions and mass constriants

2025/07/17 by Jianjun, Zhang, Xuexiu Zhong, Xuexiu, Zhong +2
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Optical properties and cooling technologies in crystalline materials #Perovskite Materials and Applications

paper · pdf · doi:10.48550/arxiv.2507.13172

openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We are concerned with the following system of two coupled time-independent Gross-Pitaevskii equations \begincases -Δu+λ₁ u=μ₁|u|^p-2u+να|u|^α-2|v|^βu ~\hboxin~ \R^N,
-Δv+λ₂ v=μ₂|v|^q-2v+νβ|u|^α|v|^β-2v ~\hboxin~ \R^N, \endcases which arises in two-components Bose-Einstein condensates and involve attractive Sobolev subcritical or critical interactions, i. e., ν>0 and α+β≤ 2^*. This system is employed by seeking critical points of the associated variational functional with the constrained mass below ∫_ℝ^N|u|² \rm dx=a, ∫_ℝ^N|v|² \rm dx=b. In the mass mixed case, i. e., 2

Citations

• Normalized ground states for a coupled Schrödinger system: Mass super-critical case
• Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
• Multiple normalized solutions for a Sobolev critical Schrödinger equation
• Normalized ground states for semilinear elliptic systems with critical and subcritical nonlinearities
• Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
• Existence and orbital stability of standing waves for nonlinear Schrödinger systems
• Normalized solutions for nonlinear Schrödinger systems

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