Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Soliton stability in birefringent optical fibers : analytical approach

Propagation of short pulses in birefringent optical fibers is considered in the framework of two coupled nonlinear Schr8dinger equations. When the amplitudes of the pulses belonging to different polarizations are equal, we propose a simple analytical explanation of the amplitude threshold for the capture of two partial pulses into a coupled two-component pulse. Our approach is based on a solito...

Stochastic algorithms for discontinuous multiplicative white noise.

Stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral. This fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories. Moreover, if the multiplicative noise function is not continuous then the standard algorithms cannot be used. We present an ...

Exact Solutions for Wave Propagation in Birefringent Optical Fibers

We carry out a group-theoretical study of the pair of nonlinear Schrödinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to provide examples of specific exact solutions. Among them, we obtain the soliton profile, which is related to the coordinate translations and the constant change of ph...

Stochastic heat equation with white-noise drift

Perturbation of Stochastic Boussinesq Equations with Multiplicative White Noise

The Boussinesq equation is a mathematics model of thermohydraulics, which consists of equations of fluid and temperature in the Boussinesq approximation.The deterministic case has been studied systematically by many authors (e.g., see [1– 3]). However, in many practical circumstances, small irregularity has to be taken into account.Thus, it is necessary to add to the equation a random force, wh...