New synchronized solutions for linearly coupled Schrodinger systems

In this paper, we consider the following linearly coupled Schrodinger system: { -Delta u + P(|y|)u = u3 + lambda(|y|)v in R3, -Delta v +Q(|y|)v = v3 + lambda(|y|)u in R3, where P(|y|), Q(|y|) and lambda(|y|) are positive radial potentials such that lambda(|y|) < min{P(|y|), Q(|y|)}. Motivated by the work of Duan and Musso [9], we use the Lyapunov-Schmidt reduction method to construct new synchronized solutions of the problem (P epsilon) with more complex concentration structure than the results in Wei, Yan [26] and Peng, Wang [23], when P(|y|), Q(|y|) and lambda(|y|) satisfy some decay assumptions at infinity. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, a linearly coupled Schrodinger system is studied, and new synchronized solutions with more complex concentration structure are constructed using the Lyapunov-Schmidt reduction method under certain decay assumptions at infinity.