The truncation model of the derivative nonlinear Schrödinger equation

G. Sánchez-Arriaga, Tohru Hada, Y. Nariyuki

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    Abstract

    The derivative nonlinear Schrödinger (DNLS) equation is explored using a truncation model with three resonant traveling waves. In the conservative case, the system derives from a time-independent Hamiltonian function with only one degree of freedom and the solutions can be written using elliptic functions. In spite of its low dimensional order, the truncation model preserves some features from the DNLS equation. In particular, the modulational instability criterion fits with the existence of two hyperbolic fixed points joined by a heteroclinic orbit that forces the exchange of energy between the three waves. On the other hand, numerical integrations of the DNLS equation show that the truncation model fails when wave energy is increased or left-hand polarized modulational unstable modes are present. When dissipative and growth terms are added the system exhibits a very complex dynamics including appearance of several attractors, period doubling bifurcations leading to chaos as well as other nonlinear phenomenon. In this case, the validity of the truncation model depends on the strength of the dissipation and the kind of attractor investigated.

    Original languageEnglish
    Article number042302
    JournalPhysics of Plasmas
    Volume16
    Issue number4
    DOIs
    Publication statusPublished - May 11 2009

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    nonlinear equations
    approximation
    Hamiltonian functions
    elliptic functions
    period doubling
    numerical integration
    traveling waves
    chaos
    dissipation
    degrees of freedom
    orbits
    energy

    All Science Journal Classification (ASJC) codes

    • Condensed Matter Physics

    Cite this

    The truncation model of the derivative nonlinear Schrödinger equation. / Sánchez-Arriaga, G.; Hada, Tohru; Nariyuki, Y.

    In: Physics of Plasmas, Vol. 16, No. 4, 042302, 11.05.2009.

    Research output: Contribution to journalArticle

    Sánchez-Arriaga, G. ; Hada, Tohru ; Nariyuki, Y. / The truncation model of the derivative nonlinear Schrödinger equation. In: Physics of Plasmas. 2009 ; Vol. 16, No. 4.
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