Abstract
The effect of formation of asymptotically stable solitary waves (ASSW) in an amplifying dispersive medium with frequency-dependent linear amplification, nonlinear losses, and nonlinear refractive index is predicted. All the parameters of the ASSW are invariants of the medium. The method developed is based on formalism of the Fokker-Planck equation describing a pulse dynamics in the presence of noise. The stability is proved by Lyapunov's method. It was found that the ASSW is described by the Euler-Lagrange equation defined by a minimum of the effective potential being the Lyapunov function. It was found that the bright solitary wave is unstable whereas the dark solitary wave is asymptotically stable.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical review. A, Atomic, molecular, and optical physics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
