Energy transfer for solutions to the nonlinear Schrödinger equation on irrational tori

Abstract

We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schrödinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the analytic study with numerical experimentation. As a biproduct of our investigation we also prove that the quasi-resonant part of the NLS initial value problem we consider, in both the focusing and defocusing case, is globally well-posed for initial data of finite mass.

References in corpus (4)

• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrodinger Equations on $\mathbb{R}$
• Energy cascades for NLS on the torus
• The Effect of Discrete Resonant Manifold Structure on Discrete Wave Turbulence

Cited by in corpus (1)

• On the Properties of Energy Flux in Wave Turbulence