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Dispersion estimates for fourth order Schrödinger equations. (English. Abridged French version) Zbl 0942.35160
Summary: Motivated by the study of the fourth-order nonlinear Schrödinger equations introduced by V. Karpman [Phys. Rev. E 53, R1336–R1339 (1996)] we give dispersion estimates for the linear group associated to \(i\partial_t +\Delta^2\pm\Delta\).

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
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