On the energy exchange between resonant modes in nonlinear Schrödinger equations

Benoit Grebert, Carlos Villegas-Blas

We consider the nonlinear Schrödinger equation $$i{\psi }_t=-{\psi }_{xx}\pm 2\cos 2x|\psi {|}^2\psi ,x\in S^1,t\in \mathbb{R}$$ and we prove that the solution of this equation, with small initial…