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Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-7269-5241
2006 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 7Article in journal (Refereed) Published
Abstract [en]

We study the long-time behavior of solutions to the Korteweg-de Vries-type equation partial derivative(t)u=-partial derivative(x)(partial derivative(2)(x)u+f(u)-b(t,x)u), with initial conditions close to a stable, b=0 solitary wave. The coefficient b is a bounded and slowly varying function, and f is a nonlinearity. For a restricted class of nonlinearities, we prove that for long time intervals, such solutions have the form of the solitary wave, whose center and scale evolve according to a certain dynamical law involving the function b(t,x), plus an H-1(R)-small fluctuation. The result is stronger than those previously obtained for general nonlinearities f.

Place, publisher, year, edition, pages
2006. Vol. 47, no 7
Keyword [en]
nonlinear schrodinger-equations, devries equation, asymptotic stability, model-equations, excited-states, solitons, kdv, scattering, existence, limit
URN: urn:nbn:se:kth:diva-15883DOI: 10.1063/1.2217809ISI: 000239423800015ScopusID: 2-s2.0-33746839181OAI: diva2:333925
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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