We demonstrate experimentally the formation and stable propagation of bound soliton pairs in a highly nonlinear photonic crystal fiber. The bound pairs occur at a particular power as the consequence of high-order soliton fission. They propagate over long distances with constant inter-soliton frequency and time separation. During propagation, the soliton self-frequency shift causes the central f...

This is a survey on Chaos in Partial Differential Equations. First we classify soliton equations into three categories: 1. (1+1)-dimensional soliton equations, 2. soliton lattices, 3. (1+n)-dimensional soliton equations (n ≥ 2). A systematic program has been established by the author and collaborators, for proving the existence of chaos in soliton equations under perturbations. For each categor...

We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization...

It is well known that additional low-frequency waves arise when a second ion population is added to a plasma normally consisting of protons and electrons. Here, we investigate stationary structures streaming with a sub-fast speed in such a bi-ion plasma. It is shown that in addition to the usual “solitons”, which have already been described for a single-ion plasma, a new type of stationary stru...

The scenarios of achieving effective ionospheric modification are summarized and the likely physical processes engaging linear and nonlinear mode conversions through plasma inhomogeneity and nonlinearity are revealed. Parametric instabilities, which are the directly relevant processes to achieve effective heating of the ionospheric F region, are formulated and analyzed. The threshold fields and...

The one-dimensional oblique propagation of magnetohydrodynamic waves with arbitrary amplitudes in a Hall plasma with isotropic pressure is studied under assumption that the plasma β is large. It is shown that the wave evolution is described by the derivative nonlinear Schrödinger equation (DNLS).

One important discovery in the twentieth century physics is the natural formation of a coherent or a well-ordered structure in continuous media, in contrary to degradation of the state as predicted earlier from the second law of thermodynamics. Here nonlinearity plays the essential role in its process. The discovery of soliton, a localized stable wave in a nonlinear and dispersive medium and th...

We investigate simulations of exact solutions of the stochastic Dr. Herman Numerical Realizations of Solutions f the Stochastic KdV Equation Exact Solution of Stochastic KdV Wadati 1983 The One Soliton Solution Under Noise Statistical Averages The Exact Solution for < u(x, t) > via the Diffusion Equation Solving the Diffusion Equation The Damped Stochastic KdV Asymptotics Numerical Simulation o...

An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characte...

Based on the factorization of soliton equations into two commuting integrable xand t-constrained flows, we derive N -soliton solutions for mKdV equation via its xand t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.