Multiple Soliton Interactions Research Articles

Transformation and interactions among solitons in metamaterials with quadratic-cubic nonlinearity and inter-model dispersion

In this paper, we investigate multiple soliton interactions and other solitary wave solutions (SWS) for a perturbed nonlinear Schrödinger equation (NLSE) with negative index material having quadratic-cubic nonlinearity (NLSE-QCN). Due to its high order dispersion term, this model yields sub-picosecond impulses useful in mode-locked ring lasers. Hirota bilinear method (HBM) will be used to study soliton interaction. By controlling the parameters, we will obtain [Formula: see text], [Formula: see text], parabolic and anti-parabolic, butterfly, bright and dark shaped solitons. On the other hand, we will obtain some other solitary wave solutions with the help of Sine-Gordon expansion (SGE) scheme.

Higher-order rogue wave solutions to the Kadomtsev–Petviashvili 1 equation

We construct a family of eigenfunction solutions of the Lax pair of the Kadomtsev–Petviashvili 1 (KP1) equation, which is expressed in terms of the Taylor coefficients of a fundamental exponential function associated with the Lax pair. Using the binary Darboux transformation, the higher-order rogue waves on a solitonic background of the KP1 equation are obtained by multiple soliton interactions. In fact, these solitons can evolve to significant and strongly localized transient waves during directional evolution, similarly to KP2 shallow-water interactions. We conjecture that the nth-order rogue wave solution evolves in the form of a triangular extreme wave pattern that consists of n(n+1)2 solitonic lumps in the intermediate time, while only n+1 parallel line solitons possessing equal height are present before and after the initiation of collision dynamics. Such fascinating higher-order rogue waves have not yet been reported in the context of this 2+1 dimensional integrable system. These exact solutions are particularly relevant for the fundamental understanding of extreme wave events in a variety of physical systems, such as plasma and solids.

Interaction properties of soliton molecules and Painleve analysis for nano bioelectronics transmission model

Microtubules (MTs) are series of protein and protofilaments. These are very important in cell divisioning, designing and nonlinear phenomena in the field of engineering and science. In this article, we study multiple soliton interactions with the help of Hirota bilinear method. We also study dromions for MTs model with the help of the extended $$(G'/G)$$ -expansion method. At the end, we will discuss integrability of model through the Painleve analysis.

Multiple Soliton Interactions on the Surface of Deep Water

The paper presents the long-time dynamics with multiple collisions of breathers in the super compact Zakharov equation for unidirectional deep water waves. Solutions in the form of breathers were found numerically by the Petviashvili method. In the terms of envelope and the assumption of the narrow spectral width the super compact equation turns into the well known exact integrable model—nonlinear Schrödinger equation, and the breather solution in this case turns into envelope soliton. The results of numerical simulations show that two main scenarios of long-time dynamics occur during numerous collisions of breathers. In the first case, one of the breathers regularly takes a number of particles from the other one at each collision and in the second one a structure resembling the bi-soliton solution of nonlinear Schrödinger equation arises during the collision. Despite these scenarios, it is shown that after numerous collisions the only one breather having initially a larger number of particles remains.

Effect of high-order dispersion on three-soliton interactions for the variable-coefficients Hirota equation.

The interactions of multiple solitons show different properties with two-soliton interactions. For the difficulty of deriving multiple soliton solutions, it is rare to study multiple soliton interactions analytically. In this paper, three-soliton interactions in inhomogeneous optical fibers, which are described by the variable coefficient Hirota equation, are investigated. Via the Hirota bilinear method and symbolic computation, analytic three-soliton solutions are obtained. According to the obtained solutions, properties and features of three-soliton interactions are discussed by changing the third-order dispersion (TOD) and other relevant coefficients, and some plentiful structure of three-soliton interactions are presented for the first time. The influences of TOD on the intensity and propagation distance of solitons are described, which can be used to realize the soliton control. Besides, the method that can achieve the phase reverse of solitons is suggested, and bound states of three solitons are observed, which have potential applications in the mode-locked fiber lasers. Furthermore, comparing to two-soliton interactions, a novel phenomenon of three-soliton interactions with a strong phase shift at x=0 is revealed, which is potentially useful for optical logic switches.

Modulation instability of ion acoustic waves, solitons, and their interactions in nonthermal electron-positron-ion plasmas

The propagation of ion acoustic waves in plasmas composed of ions, positrons, and nonthermally distributed electrons is investigated. By means of the reduction perturbation technique, a nonlinear Schrödinger equation is derived and the modulation instability of ion acoustic wave is analyzed, where the nonthermal parameter is found to be of significant importance. Furthermore, analytical expressions for the bright and dark solitons are obtained, and the interaction of multiple solitons is discussed.

Interactions between polarization-division multiplexing solitons and its suppression with nonlinear gain

In a polarization-division multiplexing soliton system, the multiple soliton interactions are studied numerically, the effects of soliton interactions on timing jitter are analyzed, and a countermeasure using nonlinear gain to suppress the soliton interactions is developed with the help of computer modeling. It is found that the mutual interactions between neighboring solitons cause soliton transmission instability and lead to timing jitter. The interactions of more than two solitons are stronger than that of two solitons. Therefore, the maximum transmission distance limited by the soliton interactions should be inferred from the collision distance of multiple soliton interactions, not the mutual interactions of two solitons. Nonlinear gain combined with a filter is suggested to effectively suppress the soliton interactions and stabilize soliton propagation.

Darboux transformations of classical Boussinesq system and its multi-soliton solutions

In this Letter, we present the third kind of Darboux transformation of the classical Boussinesq system, and discuss its relationship with the two basic Darboux transformations. By applying the Darboux transformations, we obtain the solutions of multiple soliton interactions, including overtaking and head-on collisions.

Detection and estimation of multiplexed soliton signals

Solitons are eigenfunction solutions to certain nonlinear wave equations that arise in a variety of natural and man-made systems. Their rich properties and tractability make them an intriguing component of such systems, often describing the large-scale or long-term behavior of natural systems, or the information content in certain communication or signal processing systems. However, it is often difficult to detect or estimate the parameters of solitons in such systems due to the presence of strong nonsoliton components or the nonlinear interaction of multiple solitons. The objective of this paper is to develop and investigate the detection and estimation of soliton signals. As a framework for this study, we consider using these nonlinear systems as both signal generators and signal processors in a form of multiplexed soliton communication. In contrast to more conventional uses of solitons in a communications context, our communication system uses soliton systems for signal generation and multiplexing for transmission over traditional linear channels. In addition to their mathematical tractability and the simplicity of the analog circuits used to generate and process them, we show that the soliton signal dynamics may also provide a mechanism for decreasing transmitted signal energy while enhancing signal detection and parameter estimation performance.

Multiple soliton interactions in a polarization–division multiplexing system

We numerically study multiple soliton interactions in a polarization–division multiplexing transmission system. It is found that, unlike the transmission system of solitons with the same polarization, the two soliton interaction is not the strongest compared to the interaction of more than two solitons. Therefore, the maximum transmission distance limited by the interaction of solitons cannot be inferred by the collision distance of two solitons in a polarization–division multiplexing system and the interactions of more solitons must be considered.