Two-dimensional solitary waves in media with quadratic and cubic nonlinearity

Ole Bang, Yuri S. Kivshar, Alexander V. Buryak, Alfredo De Rossi, Stefano Trillo

    Research output: Contribution to journalArticlepeer-review

    69 Citations (Scopus)

    Abstract

    We determine the existence and stability regimes of bright [formula presented]-dimensional spatial solitary waves in media with quadratic (or [formula presented]) and focusing cubic nonlinearities. We derive a necessary criterion for linear stability of these solitons, and use it to show that the quadratic nonlinearity enables stable solitons to exist when the cubic nonlinearity is sufficiently weak. We discuss why the Vakhitov-Kolokolov criterion for stability in [formula presented] systems is only a necessary criterion, and show an example where it fails. We further derive and study a simple adiabatical model for the soliton dynamics close to the instability threshold. Finally, we study the interesting dynamics of the solitons in the unstable regime, where we demonstrate the existence of two different limits described by nonlinear Schrödinger equations.

    Original languageEnglish
    Pages (from-to)5057-5069
    Number of pages13
    JournalPhysical Review E
    Volume58
    Issue number4
    DOIs
    Publication statusPublished - 1998

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