scholarly journals Stationary solutions to cubic nonlinear Schrödinger equations with quasi-periodic boundary conditions

2020 ◽  
Vol 53 (38) ◽  
pp. 385204 ◽  
Author(s):  
Andrea Sacchetti
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Stationary Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations

1998 ◽  
Vol 128 (6) ◽  
pp. 1249-1260 ◽  
Author(s):  
Silvia Cingolani ◽  
Margherita Nolasco
Keyword(s):  
Periodic Boundary ◽  
Periodic Potential ◽  
Periodic Boundary Conditions ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Stationary States ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Semiclassical States

For a class of nonlinear Schrodinger equations, we prove the existence of semiclassical stationary states with possibly infinitely many concentration points. As h → 0, these states concentrate near critical points of the potential. Furthermore, for periodic potential, these states can be constructed to satisfy periodic boundary conditions.

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