Soliton propagation and some related parameter in a photorefractive crystal are considered. This study analyzes the soliton propagation on a photorefractive crystal having both linear and quadratic electro-optical effects through a time-dependent model of nonlinear dynamics equation using the numerical split-step Fourier method. In conducting analysis, we apply various models of ansatz as initial conditions of the optical beam envelope. Based on the studies conducted, ansatz influences the soliton propagation pattern in the photorefractive crystals. Besides, we found ansatz in secant-hyperbolic and Gaussian functions as the most appropriate model for realizing solitons in crystals. Finally, the photorefractive effect supports the evolution of soliton before it achieved a level of stability.

Benchmarking of the numerical split-step Fourier method in solving a soliton propagation equation in a nonlinear optical medium is considered. This study is carried out by comparing the solutions calculated by numerics with those obtained by analytics. In particular, the soliton propagation equation used as the object of observation is the nonlinear Schrödinger (NLS) equation, which describes optical solitons in optical fiber. By using the split-step Fourier method, we show that the split-step Fourier method is accurate. We also confirm that the nonlinear and dispersion parameters of the optical fiber influence the soliton propagation.

In this study, we investigate the viscous effect by adding solvent potential into Hamiltonian Peyrard-Bishop DNA model. The dynamics of the modified Peyrard-Bishop DNA model is also considered in time-dependent thermal friction, namely Nose-Hoover Thermostat. Equation of motion formulate by using an analytical method, then solved using a numerical method. We show the pattern of phase space diagrams of the DNA dynamics in each variation of viscous and temperature, the movement of base pairs at a specific temperature, and the thermostat’s energy fluctuation that affects DNA dynamics.

Solitons are wave phenomena or pulses that can maintain their shape stability when propagating in a medium. In optical fibers, they become general solutions of the Non-Linear Schrödinger Equation (NLSE). Despite its mathematical complexity, NLSE has been an interesting issue. Soliton analysis and mathematical techniques to solve problems of the equation keep doing. Yan Chen (2022) introduced them based on bilinear formula for the case of the generalized NLSE extended models into third and fourth-order dispersions and cubic-quintic nonlinearity. In this paper, we review the form of the bilinear formula for the case. We re-observed a one-soliton solution based on the formula and verified the work of the last researcher. Here, the mathematical parameters of position α(0) and phase η are verified to become features of change in horizontal position and phase of one soliton in the (z, t) plane during propagation. In addition, we notice the soliton has established stability. Finally, for the condition Kerr effect focusing or the group velocity dispersion β2 more dominates, we present like the soliton trains in optical fibers under modulation instability of plane wave.

No abstract