Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions

Adrian Ankiewicz, Yan Wang, Stefan Wabnitz, Nail Akhmediev

    Research output: Contribution to journalArticlepeer-review

    205 Citations (Scopus)

    Abstract

    We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian- Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

    Original languageEnglish
    Article number012907
    JournalPhysical Review E
    Volume89
    Issue number1
    DOIs
    Publication statusPublished - 9 Jan 2014

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