Bifurcation analysis of the propagation of femtosecond pulses for the Triki-Biswas equation in monomode optical fibers

Bifurcation analysis of the propagation of femtosecond pulses for the Triki–Biswas (TB) equation in monomode optical fibers is reported for the first time. Bifurcation of phase plots of the dynamical system is dispensed using phase plane analysis through symbolic computation. It is observed that the TB equation supports femtosecond solitary pulse, periodic pulse, superperiodic pulse, kink and anti-kink pulses, which are presented through time series plot numerically. Analytical forms of the femtosecond solitary pulses are obtained. This contribution may be applicable to interpret the dynamical behavior of various femtosecond pulses in monomode optical fibers beyond the Kerr limit.

Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

Traveling and solitary waves in monodisperse and dimer granular chains

We provide a review of propagating traveling waves and solitary pulses in uncompressed one-dimensional ([Formula: see text]) ordered granular media. The first such solution in homogeneous granular media was discovered by Nesterenko in the form of a single-hump solitary pulse with energy-dependent profile and velocity. Considering directly the discrete, strongly nonlinear governing equations of motion of these media (i.e., without resorting to continuum approximation or homogenization), we show the existence of countably infinite families of stable multi-hump propagating traveling waves with arbitrary wavelengths. A semi-analytical approach is used to study the dependence of these waves on spatial periodicity (wavenumber) and energy, and to show that in a certain asymptotic limit, these families converge to the single-hump Nesterenko solitary wave. Then the study is extended in dimer granular chains composed of alternating “heavy” and “light” beads. For a set of specific mass ratios between the light and heavy beads, we show the existence of multi-hump solitary waves that propagate faster than the Nesterenko solitary wave in the corresponding homogeneous granular chain composed of only heavy beads. The existence of these waves has interesting implications in energy transmission in ordered granular chains.

Appearance of an ensemble solitary pulse train in transient backward stimulated Raman scattering

A self-similarity approximation model for three-wave resonant interaction in transient backward stimulated Raman scattering (BSRS) was derived. Interestingly, as its asymptotic solution, the train of solitary backward Raman pulse train is possibly formed. This result can be considered as an increment of “single” soliton observed previously [A. Abdolvand et al., Phys. Rev. Lett 103, 183902 (2009)].