This article concerns the standing waves of a linearly coupled Schrodinger system which arises from nonlinear optics and condensed matter physics. The coefficients of the system are spatially dependent and have a mixed behavior: they are periodic in some directions and tend to positive constants in other directions. Under suitable assumptions, we prove that the system has a positive ground state. In addition, when the L-infinity-norm of the coupling coefficient tends to zero, the asymptotic behavior of the ground states is also obtained.
Submitted January 11, 2016. Published January 5, 2017.
Math Subject Classifications: 35B40, 35J47, 35J50.
Key Words: Linearly coupled Schrodinger system; ground states; asymptotic behavior.
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| Haidong Liu |
College of Mathematics, Physics and Information Engineering
Zhejiang 314001, China
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