A “Localized Pulse–Moving Front” pair in a system of coupled complex Ginzburg–Landau Equations

A system of nonlinearly coupled complex Ginzburg–Landau equations, CGLEs, serves as a simple model for the dynamics of pulse propagation in dissipative, inhomogeneous media under the combined influence of dispersion, self and cross phase modulations, linear and nonlinear gain or loss. A solitary pulse (SP) is a localized wave form, and a kink or a front refers to a transition connecting two constant, but unequal, asymptotic states. Exact expressions for a “solitary pulse–kink” pair are obtained by a modified Hirota bilinear method. Parameters for these wave configurations are governed by a system of six algebraic equations, allowing the amplitudes, frequencies, and velocities to be determined. Exact solutions for special cases of the dispersive and nonlinear coefficients are obtained by computer algebra software. Copyright © 2010 The Physical Society of Japan. The final, definitive version of this paper has been published in Journal of the Physical Society of Japan, 79(12), No. 124003. The published version is located at: http://dx.doi.org/10.1143/JPSJ.79.124003