Self-frequency shift and nonlinear interaction of equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering

In this work we study numerically the self-frequency shift of the equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering (IRS). It has been established that the stationary value of the central frequency of solutions, which appears as a result of the collective action of these physical effects, is a linearly increasing function of the Raman parameter γ for the solution of Tsoy and Akhmediev (Phys Lett A 343:17–422, 2005), Tsoy et al. (Phys Rev E 73:036621, 2006), and the quadratic function of γ for the parameters used in Uzunov et al. (Phys Rev E 90:042906, 2014). We have found a complete suppression of the self-frequency shift of the equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and IRS below and at the point of the Poincare–Andronov–Hopf bifurcation (PAHB) (Uzunov et al. in Phys Rev E 90:042906, 2014). We have numerically observed stable pairs and sequences of equidistant equilibrium solutions and pulsating solutions propagating in the presence of linear and nonlinear gain, spectral filtering, and IRS below and at the point of the PAHB. The pairs and equidistant sequences of pulsating solutions at the point of bifurcation require larger initial separation and exist at smaller distances of propagation than the pairs and equidistant sequences of the equilibrium solutions below the point of bifurcation.