Virtual Community of Pathological Anatomy (University of Castilla La Mancha)· 2017
A natural constraint approach to normalized solutions of nonlinear SchrA¶dinger equations and systems
- 278citations
- 2017year
Short summary
A new natural constraint method guarantees normalized solutions for nonlinear Schrödinger systems, revealing phase separation as a parameter approaches zero.
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Key points
- A natural constraint method is introduced for nonlinear Schrödinger systems.
- Guarantees existence of normalized solutions for prescribed positive parameters and a negative cross-interaction term.
- Solutions exhibit phase separation as the cross-interaction parameter approaches negative infinity.
- Method adaptable to scalar nonlinear Schrödinger equations, simplifying existing proofs.
AI-generated from the title and abstract; the full text is not read.
Abstract
The paper deals with the existence of normalized solutions to the system âÎuâλ1u=Î1⁄41u3+Î2uv2in R3âÎvâλ2v=Î1⁄42v3+Î2u2vin R3â«R3u2=a12andâ«R3v2=a22 for any Î1⁄41,Î1⁄42,a1,a2>0 and Î2<0 prescribed. We present a new approach that is based on the introduction of a natural constraint associated to the problem. We also show that, as Î2âââ, phase separation occurs for the solutions that we find. Our method can be adapted to scalar nonlinear Schrödinger equations with normalization constraint, and leads to alternative and simplified proofs to some results already available in the literature.
The authors' abstract, as published at the source. Virtual Community of Pathological Anatomy (University of Castilla La Mancha), 2017 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics