Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation

Mathieu Colin (1, 2, 3) , Tatsuya Watanabe (4)

1 Bordeaux INP - Institut Polytechnique de Bordeaux
2 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
3 IMB - Institut de Mathématiques de Bordeaux
4 Kyoto Sangyo University

In this paper, we study the nonlinear Schrödinger equation coupled with the Maxwell equation. Using energy methods, we obtain a local existence result for the Cauchy problem.

Mots clés: Schrödinger-Maxwell system; Cauchy problem; Symmetric hyperbolic system; Energy method

Domaines: Equations aux dérivées partielles [math.AP]

Mathieu Colin, Tatsuya Watanabe. Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation. 2018. ⟨hal-01928694⟩