Standing waves for coupled nonlinear Schrödinger equations with decaying potentials

Journal Article · Fri Nov 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4833795· OSTI ID:22251789

Chen, Zhijie; Zou, Wenming ^[1]

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1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084 (China)

We study the following singularly perturbed problem for a coupled nonlinear Schrödinger system which arises in Bose-Einstein condensate: −ε{sup 2}Δu + a(x)u = μ{sub 1}u{sup 3} + βuv{sup 2} and −ε{sup 2}Δv + b(x)v = μ{sub 2}v{sup 3} + βu{sup 2}v in R{sup 3} with u, v > 0 and u(x), v(x) → 0 as |x| → ∞. Here, a, b are non-negative continuous potentials, and μ{sub 1}, μ{sub 2} > 0. We consider the case where the coupling constant β > 0 is relatively large. Then for sufficiently small ε > 0, we obtain positive solutions of this system which concentrate around local minima of the potentials as ε → 0. The novelty is that the potentials a and b may vanish at someplace and decay to 0 at infinity.

• OSTI ID: 22251789
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
COUPLING CONSTANTS
EQUATIONS
NONLINEAR PROBLEMS
POTENTIALS
STANDING WAVES