Steady Solitons Research Articles

Macro-experimental study from steady soliton to chaotic lattice soliton

OVER three decades, since the wide applications of the soliton phenomena in almost all the physical fields, the theoretical, experimental and applied studies of the soliton have become an active research topic. The direct macro-observation of the soliton phenomana is one of the important problems. Since the observation of Wu et al. on the nonpropagating fluid solitons in 1984, the nonlinear systems on the vibratmg table have offered us a good experimental field. Some nonlinear excitations of the macro-monatomic lattice have been observed by Denardo et al. Ref. reported the observation of the localized structure of the granular sys-

Soliton evolution and radiation loss for the nonlinear Schrödinger equation.

The transient evolution of general initial pulses into solitons for the nonlinear Schr\"odinger (NLS) equation is considered. By employing a trial function which consists of a solitonlike pulse with variable parameters plus a linear dispersive term in an averaged Lagrangian, ordinary differential equations (ODE's) are derived which approximate this evolution. These approximate equations take into account the effect of the generated dispersive radiation upon the pulse evolution. Specifically, in the approximate ODE's the radiation acts as a damping which causes the pulse to decay to a steady soliton. The solutions of the approximate ODE's are compared with numerical solutions of the NLS equation and are found to be in very good agreement. In addition, the potential implications for obtaining improved approximate ODE models for soliton propagation in optical fibers and other devices governed by NLS-type equations, such as soliton logic gates, are discussed.

Generation of solitons in a nonlinear periodic medium

We derive a simple analytical expression for the modulational instability of two counterpropagating waves in a periodic nonlinear structure. Numerical studies reveal that the nonlinear development of this instability leads to time-recurrent energy storage in the form of steady solitons and to soliton train emission from both ends of the filter.

Transition from soliton to chaos in nonlinear inhomogeneous media

The nonlinear Schrödinger equation with additional terms modeling inhomogeneity of the medium and external driving, has been solved numerically to demonstrate the route of transition from steady state soliton to chaotic emission of solitons in inhomogeneous media.

Damping of solitons in bubble media

The author considers the problem of damping of solitons in a bubble medium because of viscosity and interphase heat and mass transfer nonequilibrium on the assumption that their evolution is described by successive interchange of steady soliton solutions. The changes in the amplitude of the solitons obtained from analytical expressions are compared with the available experimental data.