Nonlinear Fractional Schrödinger Equations coupled by power-type nonlinearities

2021/11/09 by Eduardo Colorado, Colorado, Eduardo, Alejandro Ortega +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.05227

Abstract

In this work we study the following class of systems of coupled nonlinear fractional nonlinear Schrödinger equations, \ (-Δ)^s u₁+ λ₁ u₁= μ₁ |u₁|^2p-2u₁+β|u₂|^p |u₁|^p-2u₁ \quadin ℝ^N,
(-Δ)^s u₂ + λ₂ u₂= μ₂ |u₂|^2p-2u₂+β|u₁|^p|u₂|^p-2u₂ \quadin ℝ^N, . where u₁, u₂∈ W^s,2(ℝ^N), with N=1, 2, 3; λ_j, μ_j>0, j=1,2, β∈ ℝ, p≥ 2 and (p-1)/(2p)N0 for j=1,… ,m≥ 3, the coupling parameters β_jk=β_kj∈ ℝ for j,k=1,…,m, j≠ k. For this system we prove similar results as for m=2, depending on the values of the parameters β_jk, p, λ_j,μ_j, (for j,k=1,…,m, j≠ k).

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