Exact conditions for existence of homoclinic orbits in the fifth-order KdV model

    Authors

    A. Tovbis;D. Pelinovsky

    Comments

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    Abbreviated Journal Title

    Nonlinearity

    Keywords

    DIFFERENTIAL-EQUATIONS; WATER-WAVES; ORDERS; ASYMPTOTICS; SOLITONS; Mathematics, Applied; Physics, Mathematical

    Abstract

    We consider homoclinic orbits in the fourth-order equation v((iv)) + (1- epsilon(2)) v" - epsilon(2)v = v(2) + gamma(2vv" + v'(2)), where (gamma, epsilon) is an element of R-2. Numerical computations [CG97, C01] show that homoclinic orbits exist on certain curves gamma(epsilon) in the parameter plane (gamma, epsilon). We study the dependence. (gamma e) in the limit e - > 0 and prove that a curve gamma(epsilon) passes through the point (gamma(0), 0) only if s(gamma(0)) = 0, where s(gamma) denotes the Stokes constant for the truncated equation (with e = 0). The additional condition s'(gamma(0)) not equal 0 guarantees the existence of a unique curve. (e) passing through the point (gamma(0), 0). Every homoclinic orbit is proved to be single- humped for sufficiently small epsilon.

    Journal Title

    Nonlinearity

    Volume

    19

    Issue/Number

    10

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    2277

    Last Page

    2312

    WOS Identifier

    WOS:000241767200003

    ISSN

    0951-7715

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