Abstract

CARRASCO-MEJIA, Juliana  and  URZAGASTI, Deterlino. Localized and extended structures of the complex Ginzburg-Landau Cubic-Quintic-Septic equation associated with the parametrically forced and dissipative Sine-Gordon equation . Revista Boliviana de Física [online]. 2020, vol.36, n.36, pp.11-21. ISSN 1562-3823.

Abstract In the present work we studied the formation of localized and extended structures in a parametrically orced system near the parametric resonance and with weak dissipation described by the perturbed Sine-Gordon equation (SGP). These structures were described from the associated amplitude equation considering up to the seventh-order terms, i.e., by the complex Ginzburg-Landau Cubic - Quintic-Septic (CGL-Septic) equation associated with the SGP equation. No localized stable analytical solutions were found, however, numerical solutions were ound in the form of both localized structure and pattern. Oscillatory dynamic behavior of these structures was found due to the presence of the seventh order terms. finally, the soliton existence regions of the SGP and CGL-Septic models were compared.

Keywords : Solitons; Ginzburg; Landau theory; Nonlinear phenomena.

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