We are concerned with the decay of long time solutions of the initial value problem associated with the Schr\"odinger-Korteweg-de Vries system. We use recent techniques in order to show that solutions of this system decay to zero in the energy space. The result is independent of the integrability of the equations involved and it does not require any size assumptions.
The energy space for the Gross-Pitaevskii equation with magnetic field
Scattering Theory in the Energy Space for a Class of Hartree Equations
Asymptotic stability of lattice solitons in the energy space
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