First-order soliton perturbation theory for a generalized KdV model with stochastic forcing and damping

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    J. Phys. A-Math. Theor.

    Keywords

    KORTEWEG-DEVRIES EQUATION; QUANTUM-FIELD THEORY; DE-VRIES EQUATION; LOCAL GAUGE-THEORIES; DELTA-EXPANSION; ASYMPTOTIC STABILITY; NONPERTURBATIVE CALCULATION; WAVES; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    We discuss an application of the delta-expansion method to the soliton perturbation theory for a generalized KdV model with stochastic forcing and damping. We find that the delta-expansion method is a perturbation technique which allows one to retain a more representative linearization for a nonlinear differential equation (than comparable methods of perturbation, such as those relying on small parameters). Indeed, one primary benefit of the method is that it tends to provide much more reasonable solutions with relatively few terms (compared to standard perturbation methods) due to the more accurate linearization. We show that the method allows one to obtain first-order perturbations in which the stochastic and nonlinear contributions separate, allowing one to study each influence independently (at least, to first order). We then apply the delta-expansion method to the study of a stochastic generalized KdV model, and we show that this procedure gives a natural extension to the perturbation theory for the traditional KdV model. The actual method of computation is outlined and may be applied to a variety of generalized KdV models.

    Journal Title

    Journal of Physics a-Mathematical and Theoretical

    Volume

    44

    Issue/Number

    1

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    12

    WOS Identifier

    WOS:000285094100006

    ISSN

    1751-8113

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