Steady-state solutions for Schrodinger equations in photonic lattice
In this article, we study a nonlinear Schrodinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrodinger system which is intimately related to the Schrodinger equation. We obtain the existence of nontrivial...
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| Format: | Article |
| Language: | English |
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Texas State University
2018-05-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/109/abstr.html |
| Summary: | In this article, we study a nonlinear Schrodinger equation arising in optics.
Firstly we prove the existence of multiple solutions of this equation.
Secondly, we consider a nonlinear Schrodinger system which is intimately
related to the Schrodinger equation. We obtain the existence of
nontrivial solutions to this system and we also get some results on
its positive solutions. Finally, assuming Dirichlet or Neumann boundary
condition, we show the existence and uniqueness of positive solution to
the Schrodinger equation. |
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| ISSN: | 1072-6691 |