Soliton Self-wave Number Downshift Compensation by the Increasing Second-Order Dispersion
Dynamics of solitons in the frame of the extended nonlinear Schrödinger equation (NSE) taking into account stimulated Raman scattering (SRS) and inhomogeneous second-order dispersion (SOD) is considered. Compensation of soliton Raman self-wave number downshift in media with increasing second-order linear dispersion is shown. Quasi-soliton solution with small wave number spectrum variation, amplitude and extension are found analytically in adiabatic approximation and numerically. The soliton is considered as the equilibrium of SRS and increasing SOD. For dominate SRS soliton wave number spectrum tends to long wave region. For dominate increasing SOD soliton wave number spectrum tends to shortwave region.
KeywordsDynamics of solitons and quasi-solutions Extended nonlinear Schrödinger equation Stimulated Raman scattering Inhomogeneous second-order dispersion
This study was carried out within “The National Research University Higher School of Economics’ Academic Fund Program in 2012–2013, research grant No.11-01-0066”. This work was supported by the Russian Foundation for Basic Research (project 12-02-00436-a).
- 2.Dickey, L.A.: Soliton Equation and Hamiltonian Systems. World Scientific, New York (2005)Google Scholar
- 3.Kivshar, Y.S., Agraval, G.P.: Optical Solitons: From Fibers to Photonic Crystals. Academic, San Diego (2003)Google Scholar
- 13.Gromov, E.M., Talanov, V.I.: Sov. Phys. JETP 83, 73–79 (1996)Google Scholar
- 20.Tsitsas, N.L., Rompotis, N., Kourakis, I., Kevrekidis, P.G., Frantzeskakis, D.J.: Phys. Rev. Lett. E 79, 037601 (2009)Google Scholar
- 22.Biancalama, F., Skrybin, D.V., Yulin, A.V.: Phys. Rev. E 70, 011615 (2004)Google Scholar