A novel variational approach to pulsating solitons in the cubic-quintic Ginzburg-Landau equation

    Authors

    S. C. Mancas;S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Theor. Math. Phys.

    Keywords

    variational formalism; complex Ginzburg-Landau equation; pulsating; soliton; MODULATED AMPLITUDE WAVES; TIME-PERIODIC SOLUTIONS; DISSIPATIVE SYSTEMS; INSTABILITIES; FRONTS; PULSES; SINKS; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    Comprehensive numerical simulations of pulse solutions of the cubic-quintic Ginzburg-Landau equation (CGLE) reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary wave solutions, i.e., pulsating, creeping, snake, erupting, and chaotic solitons that are not stationary in time. They are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcation sequences of these pulses as the CGLE parameters are varied. We address the issues of central interest in this area, i.e., the conditions for the occurrence of the five categories of dissipative solitons and also the dependence of both their shape and their stability on the various CGLE parameters, i.e., the nonlinearity, dispersion, linear and nonlinear gain, loss, and spectral filtering. Our predictions for the variation of the soliton amplitudes, widths, and periods with the CGLE parameters agree with the simulation results. We here present detailed results for the pulsating solitary waves. Their regimes of occurrence, bifurcations, and the parameter dependences of the amplitudes, widths, and periods agree with the simulation results. We will address snakes and chaotic solitons in subsequent papers. This overall approach fails to address only the dissipative solitons in one class, i.e., the exploding or erupting solitons.

    Journal Title

    Theoretical and Mathematical Physics

    Volume

    152

    Issue/Number

    2

    Publication Date

    1-1-2007

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    1160

    Last Page

    1172

    WOS Identifier

    WOS:000249211500011

    ISSN

    0040-5779

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