Statistical Analysis of Cosh Gaussian Breathers in Cubic Quintic Media Possessing Hump Shaped Quintic Nonlinearity

Statistical investigation of the dynamics of cosh Gaussian (ChG) breather propagating in a cubic quintic (CQ) nonlinear medium possessing an axial hump shaped profile of quintic nonlinearity has been presented. Using moment theory approach the propagation dynamics of the breather has been reduced to an ordinary differential equation governing the evolution of the beam width of the laser beam. This allows a detailed analysis of how the beam shape parameter affects the stability and dynamical structure of the propagation dynamics of the breather. A variety of statistical and geometrical diagnostic techniques including probability density distributions, covariance matrices, recurrence structures and autocorrelation analysis are employed to investigate the underlying dynamics of the breather states. The analysis reveals that variations in the beam shape parameter of the ChG laser beam significantly modify dynamics of the breather. In particular, the transition from weak to strong nonlinear dynamics accompanied by enhanced statistical correlations and recurrence patterns has been observed.