Blow-up solutions to a class of nonlinear coupled Schrödinger systems with power-type-growth nonlinearities

2024/08/16 by Norman Noguera, Noguera, Norman
Mathematics · Physics and Astronomy · #35A01 #35B44 #35J50 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2408.09045

openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we consider a system of nonlinear Schrödinger equations whose nonlinearities satisfy a power-type-growth. First, we prove that the Cauchy problem is local and global well-posedness in L² and H¹. Next, we establish the existence of ground state solutions. Then we use these solutions to study the dichotomy of global existence versus blow-up in finite time. Similar results were presented in the reference Noguera N. and Pastor A. 2022 https://doi.org/10.1142/S0219199720500236 for the special case when the growth of the nonlinearities was quadratic. Here we will extend them to systems with nolinearities of order p (cubic, quartic and so on). Finally, we recover some known results for two particular systems, one with quadratic and the other with cubic growth nolinearities.

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