Determination of boundaries of unsteady oscillatory zone in asymptotic solutions of non-integrable dispersive wave equations

We propose a simple general method for analytic determination of the boundaries of the expanding nonlinear oscillation zone occurring in the decay of a step problem for non-integrable dispersive wave equations. A remarkable feature of the method is that it essentially uses only the dispersionless li...

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Bibliographic Details
Published inPhysics letters. A Vol. 318; no. 6; pp. 526 - 536
Main Authors El, G.A., Khodorovskii, V.V., Tyurina, A.V.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 24.11.2003
Subjects
Dispersive shock
Finite-amplitude waves
Modulation equations
Finite-amplitude waves
Dispersive shock
Modulation equations
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Summary:We propose a simple general method for analytic determination of the boundaries of the expanding nonlinear oscillation zone occurring in the decay of a step problem for non-integrable dispersive wave equations. A remarkable feature of the method is that it essentially uses only the dispersionless limit and the linear dispersion relation of the original nonlinear dispersive wave system. A concrete example pertaining to collisionless plasma dynamics is considered and complete agreement with the results of earlier numerical simulations is demonstrated.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2003.09.060