Segregated Vector Solutions for linearly coupled Nonlinear Schrödinger Systems

2013/10/07 by Chang‐Shou Lin, Shuangjie Peng, Lin, Chang-Shou +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1310.1718

openalex publication_date 2013/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following system linearly coupled by nonlinear Schrödinger equations in \R³ \-Δu_j+u_j=u³_j-\va∑_{i≠ j}^N u_i,\1cm · amp; x∈ \R³, \0.2cm
u_j∈ H¹(\R³), j=1,⋯,N, . where \va∈\R is a coupling constant. This type of system arises in particular in models in nonlinear N-core fiber. We examine the effect of the linear coupling to the solution structure. When N=2,3, for any prescribed integer ℓ≥ 2, we construct a non-radial vector solutions of segregated type, with two components having exactly ℓ positive bumps for \va>0 sufficiently small. We also give an explicit description on the characteristic features of the vector solutions.

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