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Self-similarity and asymptotic stability for coupled nonlinear Schrödinger equations in high dimensions. (English) Zbl 1236.35164

Summary: This paper is concerned with systems of coupled Schrödinger equations with polynomial nonlinearities and dimension \(n \geq 1\). We show the existence of global self-similar solutions and prove that they are asymptotically stable in a framework based on weak-\(L^{p}\) spaces, whose elements have local finite \(L^{2}\)-mass. The radial symmetry of the solutions is also addressed.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C06 Self-similar solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B06 Symmetries, invariants, etc. in context of PDEs
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