Traveling wave solutions (u, v) to a generalized Drinfel'd-Sokolov system which satisfy u = a(1)v(m) + a(0)

    Authors

    E. Sweet;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Generalized Drinfel'd-Sokolov equations; Hamiltonian formulation; Numerical solution; Nonlinear PDE; W-ALGEBRAS; DIFFERENTIAL-EQUATIONS; PERIODIC-SOLUTIONS; WILSON EQUATION; REDUCTION; OPERATORS; DEFORMATIONS; Mathematics, Applied

    Abstract

    An analysis of the coupled generalized Drinfel'd-Sokolov equations u(t) + alpha(1)uu(x) + beta(1)u(xxx) + gamma(v(delta))(x) = 0 and v(t) + alpha(2)uv(x) + beta(2)v(xxx) = 0 is performed in the case of traveling wave solutions u and v satisfying the condition u = a(1)v(m) + a(0). We are able to classify all such solutions in terms of the model parameters, and we then discuss the planar dynamics of such solutions. Numerical solutions are obtained and discussed for a variety of parameter regimes. Such results are one possible generalization of those given by Wu et al. [L. Wu, S. Chen, C. Pang, Traveling wave solutions for generalized Drinfeld-Sokolov equations, Applied Mathematical Modeling 33 (2009) 4126-4130]. (C) 2012 Elsevier Inc. All rights reserved.

    Journal Title

    Applied Mathematics and Computation

    Volume

    218

    Issue/Number

    19

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    9911

    Last Page

    9921

    WOS Identifier

    WOS:000303531500034

    ISSN

    0096-3003

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