Presence Of Nonlinear Damping Research Articles

Uniform decay rates of coupled anisotropic elastodynamic/Maxwell equations with nonlinear damping

This work is devoted to study the asymptotic behavior of the total energy associated with a coupled system of anisotropic hyperbolic models: the elastodynamic equations and Maxwell's system in the exterior of a bounded body in \mathbb{R}^3 . Our main result says that in the presence of nonlinear damping, a unique solution of small initial data exists globally in time and the total energy as well as higher order energies decay at a uniform rate as t \rightarrow + \infty .

Kink-soliton explosions in generalized Klein–Gordon equations

We investigate the dynamics of kink-solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We present different mechanisms for kink-soliton explosion and show that, in some cases while some analytically obtained conditions are satisfied, the kink-soliton breaks up becoming a permanent, extremely complex, spatiotemporal dynamics. We perform computer simulations in order to visualize and corroborate our analytical findings. The mechanisms presented for kink-soliton breakup can explain some of the phenomena that recently have been reported to occur in excitable media. Finally, we will present a way to control soliton breakup, using appropriate external perturbations.

Envelope solitons in a medium with strong nonlinear damping

The formation of microwave spin-wave envelope solitons in the ferrite film of yttrium iron garnet in the presence of strong nonlinear damping has been experimentally found and investigated. The solitons are formed due to the four-wave interactions of spin waves when the characteristic time of wave modulation-instability development is much shorter than the time for establishing the generation of short-wavelength magnons. The presence of nonlinear damping allows the excitation of spin-wave envelope solitons by means of long microwave pulses.

Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.

Role of nonlinear dissipation in soft Duffing oscillators.

The effect of a strictly dissipative force (velocity to the pth power model) on the response and bifurcations of driven, soft Duffing oscillators is considered. The method of harmonic balance is used to obtain the steady state harmonic response. An anomalous jump in the harmonic response (signifying a break in the resonance curve), obtained in the case of linearly damped, soft Duffing oscillators, is shown to persist even in the presence of nonlinear damping. It is shown that the bifurcation structure and the structure of the chaotic attractor are quite insensitive to the damping exponent p. However, the threshold values of the parameters, at which bifurcations occur, depend both on the damping index and the damping coefficient. The Melinkov criterion and an analytical criterion for the period-doubling bifurcation have been obtained in the presence of combined linear and cubic damping.

A modified approach for the application of Fokker-Plank equation to the nonlinear ship motions in random waves

An analytical method for the study of transient behaviour as well as the stationary solution of non-linear ship motion in random waves is presented. The problem of rolling motion of a ship travelling in olbique random waves is considered for the purpose of illustrating the method. The presence of nonlinear damping and restoration terms of general form is allowed. Differential equations which govern the propagation of the expected value and the variance of the motion in this case are derived, using the Fokker-Plank equation. The results are specialized to the case of a ship rolling in beam waves. Results are compared with similar results obtained by other methods. This method gives the exact stationary solution when the damping is linear.