Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

¹Ecole Nationale Supérieure Polytechnique, University of Yaounde I, PO Box 8390, Cameroon ²Department of Physics, Faculty of Science, University of Yaounde I, PO Box 812, Cameroon ³The Abdus Salam International Centre for Theoretical Physics, PO Box 586, Strada Costiera, II-34014, Trieste, Italy

Received Date: October 05, 2008

Published Date: February 28, 2009

Abstract

We investigate the dynamical behaviour of a coupled dispersionless system (CDS) by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most stable travelling waves in another situation of boundary conditions.

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