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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Interaction of solitary pulses in active dispersive–dissipative media; pp. 139–144

(Full article in PDF format) doi: 10.3176/proc.2010.2.12


Authors

Dmitri Tseluiko, Sergey Saprykin, Serafim Kalliadasis

Abstract

We examine weak interaction and formation of bound states of pulses for the generalized Kuramoto–Sivashinsky (gKS) equation, which is one of the simplest prototypes describing active media with energy supply, dissipation, dispersion, and nonlinearity. We derive a system of ordinary differential equations describing the leading-order dynamics of the pulses of the gKS equation and prove a criterion for the existence of a countable infinite or finite number of bound states. Our theory is corroborated by computations of the full equation.

Keywords

dissipative solitons, solitary-pulse interaction, bound states, generalized Kuramoto–Sivashinsky equation.

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Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December