A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence

Cédric Galusinski

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We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian ${(- Δ)}^{κ / 2}$ with $1 \leq κ \leq 2$ . Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for...