The term soliton has recently been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed. To date at least seven distinct wave systems, representing a wide range of applications in applied science, have been found to exhibit such solutions. This review paper covers the current status of soliton research, paying particular attention to the very important "inverse method" whereby the initial value problem for a nonlinear wave system can be solved exactly through a succession of linear calculations.

The soliton: A new concept in applied science

Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

https://science.sciencemag.org/content/sci/286/5444/1518.full.pdf

Optical Spatial Solitons and Their Interactions: Universality and Diversity.

Part I. Stationary waves: Scalar equation Leray-Schauder degree Existence of waves Structure of the spectrum Stability and approach to a wave Part II. Bifurcation of waves: Bifurcation of nonstationary modes of wave propagation Mathematical proofs Part III. Waves in chemical kinetics and combustion: Waves in chemical kinetics Combustion waves with complex kinetics Estimates and asymptotics of the speed of combustion waves Asymptotic and approximate analytical methods in combustion problems (supplement) Bibliography.

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Traveling wave solutions of parabolic systems

High power pulsed magnetron sputtering (HPPMS) is an emerging technology that has gained substantial interest among academics and industrials alike. HPPMS, also known as HIPIMS (high power impulse ...

High power pulsed magnetron sputtering: A review on scientific and engineering state of the art

This paper addresses the adaptive synchronization problem of the drive–driven type chaotic systems via a scalar transmitted signal. Given certain structural conditions of chaotic systems, an adaptive observer-based driven system is constructed to synchronize the drive system whose dynamics are subjected to the system’s disturbances and/or some unknown parameters. By appropriately selecting the observer gains, the synchronization and stability of the overall systems can be guaranteed by the Lyapunov approach. Two well-known chaotic systems: Rossler-like and Chua’s circuit are considered as illustrative examples to demonstrate the effectiveness of the proposed scheme. Moreover, as an application, the proposed scheme is then applied to a secure communication system whose process consists of two phases: the adaptation phase in which the chaotic transmitter’s disturbances are estimated; and the communication phase in which the information signal is transmitted and then recovered on the basis of the estimated parameters. Simulation results verify the proposed scheme’s success in the communication application.

Adaptive synchronization of chaotic systems and its application to secure communications

Using techniques from active control theory, we demonstrate that a coupled Lorenz system can be synchronized The synchronization is verified using the Simulink feature in MATLAB

Synchronization of two Lorenz systems using active control

The experiments on solitons in plasmas performed during the period 1970 to 1982 are reviewed. Suggestions for future experiments are presented.

https://iopscience.iop.org/article/10.1088/0032-1028/25/9/001/pdf

Soliton experiments in plasmas

Active and nonlinear wave propagation in electronics

Using techniques from active control theory, we demonstrate that a coupled Lorenz system can be synchronized. The application of the control elements is sequentially applied and the ensuing synchronization is displayed.

Sequential synchronization of two Lorenz systems using active control

A series of computer simulations and experiments has been performed to investigate the time evolution of an ion space-charge sheath from a solid electrode in a plasma. A large negative step potential (eΔV ≫ kTe) is applied to the boundary of a uniform plasma and the response computed. A fluid model is used for cold ions, and hot electrons in thermal equilibrium are assumed as a neutralizing background. Both the computer simulations and the experiments show the formation of an ion space-charge sheath in a few ion plasma periods and a rarefying disturbance propagating into the plasma with the ion acoustic speed. For a plane electrode this disturbance extends to the electrode, resembling a rarefaction wave as found in ordinary fluid dynamics. For cylindrical and spherical electrodes this disturbance breaks away from the sheath and propagates as an ion acoustic wave into the plasma. The addition of substantial ion-neutral collisions is found to prevent separation of the wave from the sheath. The results of th...

Karl E. Lonngren

Papers

Synchronization of two Lorenz systems using active control

Soliton experiments in plasmas

Active and nonlinear wave propagation in electronics

Sequential synchronization of two Lorenz systems using active control

Ion Acoustic Wave Excitation and Ion Sheath Evolution