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Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

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  • We consider the asymptotic behavior in time of solutions to the nonlinear Schrödinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS) as $t\to∞$.

    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B40.

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