Infinitely many segregated vector solutions of Schrodinger system

2021/09/27 by Ohsang Kwon, Kwon, Ohsang, Min-Gi Lee +3
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2109.12822

openalex publication_date 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following system of Schrödinger equations .\begincases -ΔU + λU = α₀ U³+ βUV² -ΔV + μ(y) V = α₁ V³+βU²V \endcases. in ℝ^N, N=2, 3, where λ, α₀, α₁>0 are positive constants, β∈ ℝ is the coupling constant, and μ: ℝ^N → ℝ is a potential function. Continuing the work of Lin and Peng \citelin_peng₂014, we present a solution of the type where one species has a peak at the origin and the other species has many peaks over a circle, but as seen in the above, coupling terms are nonlinear.

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