Breather-like Solitons Research Articles

Multi-soliton solutions of coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions

Abstract This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions. These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers. By analyzing the Lax pair and the Riemann–Hilbert problem, we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system. Furthermore, we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors. Through appropriate parameter selections, we observe various nonlinear phenomena, including the disappearance of solitons after interaction and their transformation into breather-like solitons, as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

Study of lump and periodic waves along with rogue waves and breathers for mathematical modeling of biological dynamical system

Globally, infectious diseases pose a significant threat. Notable cases include influenza, Hepatitis B and HIV. COVID-19, caused by the coronavirus, has been the subject of recent discussion due to its great transmissibility. This study explores the Susceptible–Infectious–Recovered (SIR) epidemic model, explaining several analytical approaches to comprehend the nonlinear incident rates and geographic dispersion. The model investigates phenomena such as M-shaped solitons, homoclinic breather-like solitons, lump waves (LWs), lump solution (LS) with one or two kinks, rogue waves (RWs), periodic waves (PWs) and periodic cross-kink waves. These solutions aid in understanding the disease spread and informing containment strategies by identifying optimal outbreak control methods. This work studies localized wave solutions in nonlinear wave equations, known as soliton solutions including the LS. RWs are characterized by unexpectedly large amplitude and rapid profile changes, drawing attention for their erratic features. PWs exhibit periodic repetitions over time and space. Besides, some type of solitons with special waveforms are the periodic cross-kink, M-shaped and homoclinic breather-like solitons. Graphical representation visualizes the behavior of these effective waves, providing insights into virus spread in specific regions over time. SIR models help identify optimal strategies for controlling outbreaks. The work adds to our understanding of epidemic dynamics by illuminating how the movement of susceptible and infected individuals affects the spread of disease.

Binary Darboux transformation and interactions of solitons for a higher-order matrix nonlinear Schrödinger equation

In this paper, we present two- and three-soliton solutions for a higher-order matrix nonlinear Schrödinger equation based on the binary Darboux transform constructed, and analyze various types of interaction properties of solitons. For the two solitons, our analytical results reveal four major features that are associated to interaction dynamics: breather-like solitons, bound-state solitons, bound states of the solitons with one/two peaks and bound states of one soliton and another soliton with breather-like structure. In addition, we graphically analyze the related properties with regard to interactions of three solitons, and seven different types of interesting appearances about soliton interactions are obtained, including shape-changing and shape-preserving interactions.

W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

We use the fractional nonlinear Schrödinger equation (FNLSE) to describe the polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms to analyze the effects of the fractional time parameter (FTP) on bright and dark solitons as well as breather-like solitons. We use the transformation hypothesis and auxiliary equations method to obtain three families of solutions such as combined bright soliton, dark solitons, and rational solitons. We have shown the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected and the soliton is unstable. Moreover, one observes the effects of fraction time on Modulation Instability (MI) gain spectra and MI bands. For certain values of the FP, it is formed sides lobes and for specific small values of the FP, both stability zone increases and amplitude of the MI gain increase while the stability zones increase. To confirm the robustness of the analytical results, we have used a numerical investigation. One exhibits the formation of breathers-like soliton with stable amplitude for small values of the FTP. It results from this study that the FP is efficient and can be used as an energy source where soliton or breathers-like soliton are involved for communication in optical fibers.

Magnetic breathers and chaotic wave fields for a higher-order [formula omitted]-dimensional nonlinear Schrödinger-type equation in a Heisenberg ferromagnetic spin chain

Ferromagnetism, whose physical properties include the Giant-Magneto resistance, spin-transfer torque, spin-Hall effect and so on, attracts researchers’ interest in the search for the spin polarizers in spin electronics. In this paper, we investigate a higher-order (2+1)-dimensional nonlinear Schrödinger-type equation for a Heisenberg ferromagnetic spin chain with the bilinear and biquadratic interaction. Magnetic breathers are derived. Conditions of the transformation from the magnetic breather to the magnetic soliton are obtained. We get the magnetic chaotic wave fields, in which the magnetic breather-like solitons and rogue waves appear. Effects of γ on the magnetic chaotic wave fields are studied: As γ increases, mean amplitude of the magnetic waves in the chaotic wave field increases, and amplitude dispersion degree decreases, where γ represents the lattice parameter.

Breather-like solitons, rogue waves, quasi-periodic/chaotic states for the surface elevation of water waves

In this paper, we investigate the surface elevation of water waves $$\eta $$ via an NLS equation under the coefficient constraint $$\omega ^{2}=gk$$ , where g is the gravity acceleration, k and $$\omega $$ are the carrier wave number and cyclic frequency, respectively. Through the Euler formula, we derive the breather-like solitons and rogue waves on the periodic background for $$\eta $$ . Breather-like solitons and rogue waves for $$\eta $$ are related with g and k. Effects of k on the breather-like solitons for $$\eta $$ are discussed analytically and graphically: Increase of k makes the decrease in the amplitudes of the breather-like solitons for $$\eta $$ . Amplitudes of the rogue waves for $$\eta $$ increase with k increasing in the position $$X=0$$ , where X denotes the spatial coordinate. Rogue waves on the periodic background for $$\eta $$ are more stable than breather-like solitons for $$\eta $$ . Multiple rogue waves of $$\eta $$ are generated from the initial rogue waves and periodic waves for $$\eta $$ with the noise perturbations in the baseband MI regime. Quasi-periodic state for $$\eta $$ is seen with $$0.523<k<0.544$$ . Chaotic state for $$\eta $$ appears with $$k<0.523$$ or $$k>0.544$$ .

Breatherlike solitons extracted from the Peregrine rogue wave.

Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breatherlike solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.

On the N-wave equations and soliton interactions in two and three dimensions

Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with ℤ 2 × ℤ 2 reduction group allow breather-like solitons. Finally it is demonstrated that RHP with sewing function depending on three variables t, x and y provides some special solutions of the N-wave equations in three dimensions.

Localized moving breathers in a 2D hexagonal lattice

We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2D hexagonal nonlinear lattice. The lattice is subject to an on-site potential in addition to longitudinal nonlinear interparticle interactions. This study investigates the prediction that stable breather-like solitons could be formed as a result of energetic scattering events in a given layered crystal and would propagate in atomic-chain directions in certain atomic planes. This prediction arose from a long-term study of previously unexplained dark lines in natural crystals of muscovite mica.

Solitary wave solutions of nonlinear equations

Abstract A general semi-analytic method is suggested to obtain the solitary wave solutions for some kinds of nonlinear equations, by the combination of the function-series method and the simulated annealing technique. The validity and reliability of the method are tested by applying it to the study of a generalized φ 4 equation. With the proper boundary and initial conditions, pulse-, kink- and breather-like solitons and their combinations are obtained.

Branching growth of ribbing patterns and the significance of concealed signals

Extending the analysis of the ribbing patterns of Recent branchiopods, pattern transformation with the progression of growth is discussed. In ribbing patterns of brachiopods, each rib grows wider and higher, and sometimes branches off. It is proposed that median patterns appear as predictable outcomes of a simple space-filling process with stochastic properties, as shown by some investigators. From the analysis by the modified Fly method, it is found that branching points are determined by deterministic long range waves (breather-like solitons) which strongly interact with one another. For these patterns, all possible Interactive Lindenmayer systems with two sided inputs of most neighbouring cells were simulated, and all patterns were classified, compared to solutions with non-linear wave equations. It is concluded that ribbing patterns with deterministic signals are realized by coupling automata between I-L system developing kinks, and cell automata developing solitons. The importance of a morphogenetic control theory involving coupling and long range signals is emphasized.