Propagation And Control Dynamics Of Nonautonomous Optical Solitons

Using the analytical (similarity reduction method) and numerical (split-step fastFourier transform algorithm and Newton’s iteration method) methods, the influence ofdispersion, nonlinearity, and amplification to the amplitude, width, and chirp of the opticalsoliton is investigated in the framework of the nonlinear Schr dinger equaiton withvariable coefficients. The precise control of optical soliton has been studied. These resultsprovide theretical foundation for the dynamical control of optical soliton, and havepotential applications for the study of solitary wave dynamics in other physical systemssuch as Bose-Einstein condensates and plasma. Main contributions of this thesis are asfollows:1. Self-similar optical pulses in competing cubic-quintic nonlinear media withdistributed coefficients.We present a systematic analysis of the self-similar propagation of optical pulsesdescribed by the generalized cubic-quintic nonlinear Schr dinger equation. Choosing therelations between the distributed coefficients appropriately, we construct the exactsolitonic similartions, the approximate Gaussian-Hermite similaritons, and the asympototiccompact similartions. The matchmatical principle for exact controlling is established, andwe reveal that proper choices of the distributed coefficients could make the unstablesolitons stable and could restrict the nonlinear interaction between the neighboring solitons.For the asympototic compact similaritons, we find their shapes can be steeper than theasympototic compact parabolic similartions.2. Optical rogue waves: Recurrence, annihilation and sustainment.We investigate optical rogue waves in nonlinear optical fiber with group-velocitydispersion, cubic nonlinearity and linear gain managements. We present conditions forcontrolling the dynamics of optical pulses via a self-similar transformation. By properly choosing the distributed coefficients, we demonstrate analytically and numerically thatrogue waves are controllable, that is, they can be restrained or even be annihilated, emergeperiodically and sustain forever. The results are of value to avoiding or utilizing roguewave.3. Exact soliton solutions and their stability control in the nonlinear Schr dingerequation with spatiotemporally modulated nonlinearity.We put forward a generic transformation, which helps to find exact soliton solutionsof the nonlinear Schr dinger equation with a spatiotemporal modulation of the nonlinearityand external potentials. As an example, we construct exact solitons for the defocusingnonlinearity and harmonic potential. When the soliton’s eigenvalue is fixed, the number ofexact solutions is determined by energy levels of the linear harmonic oscillator. In additionto the stable fundamental solitons, stable higher-order modes, describing array of darksolitons nested in a finite-width background, are also constructed. We also show how tocontrol the instability domain of the nonstationary solitons.4. Vortex solitons in defocusing media with spatially inhomogeneousnonlinearity.The analytical two-and three-dimensional vortex solitons with arbitrary values ofvorticity are constructed in the cubic defocusing media with spatially inhomogeneousnonlinearity. The values of the nonlinearity coefficients are zero near the center andincrease rapidly toward the periphery. In addition to the analytical ones, a number ofvortex solitons are found numerically. It is shown that analytical vortex solitons are stable.Also, the stability regions of the numerically constructed vortex solitons are given. Stablethree-dimensional vortex solitons with high values of vorticity are first found analyticallyand numerically.