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Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential |
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| Authors: | Johannes Giannoulis Christof Sparber |
| Affiliation: | a Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching b. München, Germany b Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany c Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany d Wolfgang Pauli Institute Vienna & Faculty of Mathematics, Vienna University, Nordbergstraße 15, A-1090 Vienna, Austria |
| Abstract: | 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 interaction of these pulses. |
| Keywords: | 81Q20 34E13 34E20 35Q55 |
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