WIAS Preprint No. 1221, (2007)
Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential
- Giannoulis, Johannes
- Mielke, Alexander
- Sparber, Christof
2010 Mathematics Subject Classification
- 81Q20 34E13 34E20 35Q55
- Nonlinear Schrödinger equation, Bloch eigenvalue problem, two scale asymptotics, modulation equations, four-wave interaction
We consider a cubic nonlinear Schrödinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses.
- J. Differential Equations, 245 (2008) pp. 939--963.