Multiple normalized solutions for a class of dipolar Gross-Pitaveskii equation with a mass subcritical perturbation

2025/07/14 by Yalin Shen, Yichen Zhang, Shen, Yalin +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2507.09893

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the existence of multiple normalized solutions to the following dipolar Gross-Pitaveskii equation with a mass subcritical perturbation \ -(1)/(2)Δu+μu+V(ε x)u + λ₁ |u|²u + λ₂(K∗|u|²)u + λ₃|u|^p-2u = 0, · amp;in ℝ³,
∫_ℝ³ |u|²dx = a²,. where a,ε>0, 2 0 is sufficiently small.

Citations

• On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions
• Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases
• Existence of solitary waves in dipolar quantum gases
• Nonlinear Schr�dinger equations and sharp interpolation estimates

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