Different Types Of Solitary Waves Research Articles

Symmetry transformations and novel solutions for the graphene thermophoretic motion equation with variable heat transmission using Lie group analysis

The single-layer graphene flake is an amazing tool in recent industry, it has many uses in biosensors, photonics and water filtration because of its outstanding electronic, thermal, and mechanical properties. In this letter, we have studied the graphene variable heat transmission thermophoretic motion (vcGT) equation using the symmetry group method. As a result, a Lie group of four vector fields is yielded. By using a linear combination of those vector fields the vcGT equation becomes a nonlinear ordinary differential equation, and by using the F-expansion technique then different types of solitary waves like periodic Jacobi elliptic waves, soliton, kink soliton and trigonometric waves were found which cover other solutions in the literature such as solitons and have additional new solutions like the periodic Jaocbi waves. Finally, we have discussed the effect of the variable heat transmission on the wave propagation for three different wave structures: Jacobi periodic wave, bright soliton and the trigonometric sec wave. It was found that in the real physical situation corresponding to the variable heat transmission the waves take a parabolic shape.

Study on chirped dark, bright solitons conversion and the effect of intermodal dispersion, self-frequency shift, and self-steepening effect on the chirping of bright, dark, and kink solitary waves

This study reveals the dynamics of short optical pulses in nonlinear media. Then, for the survival of different types of solitary waves in the nonlinear medium, the constraint relations to the physical parameters and chirps associated with each of the solitary waves are explicitly shown. We authenticate numerically all those obtained from the analytical method and show the chirping effect is saturative in nature and can be managed by changing coefficients of inter-modal dispersion, stimulated Raman scattering (SRS), and self-steepening effect. We also verify the more operative condition of intermodal dispersion.

Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation

We consider approximate, exact, and numerical solutions to the cylindrical Korteweg–de Vries equation. We show that there are different types of solitary waves and obtain the dependence of their parameters on distance. Then, we study the interaction of solitary waves of different types.

Solitary matter wave in spin-orbit-coupled Bose-Einstein condensates with helicoidal gauge potential.

We analytically and numerically study the different types of solitary wave in the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). Adopting the multiscale perturbation method, we derive the analytical bright and dark solitary wave solutions of the system, and the stationary and moving bright (dark) solitary waves are obtained. The effects of spin-orbit coupling, the helicoidal gauge potential, the momentum, the Zeeman splitting, and the atomic interactions on the solitary wave types are discussed, and it is found that the coupling of these physical parameters can manipulate different types of solitary waves in the system. The results indicate that the helicoidal gauge potential breaks the symmetric properties of the energy band of the system and adjusts the energy band structure, thus further effecting the solitary wave properties, i.e., stationary or moving solitary wave, bright, or dark solitary wave. Correspondingly, the analytical predictions for exciting stationary or moving bright (dark) solitary wave in parameter space are obtained. In particular, the helicoidal gauge potential changes the solitary wave types drastically for the weak spin-orbit coupling, i.e., in the absence of the helicoidal gauge potential, only dark (bright) solitary wave solutions exist in the system with repulsive (attractive) atomic interaction; however, in the presence of the helicoidal gauge potential, both dark and bright solitary waves can exist in the system regardless of whether the atomic interaction is repulsive or attractive. In addition, we investigate the stability of solitary waves and obtain the stability regions of different types of solitary waves by applying the linear stability analysis. The dynamic evolution results of the solitary waves by the direct numerical simulation not only validate the linear stability analysis but also confirm the analytical prediction of the solitary waves. Finally, the collision effects between solitary waves are also presented by the numerical simulation. It is shown that the interactions between solitary waves in the system have both elastic and inelastic collisions, which are closely related to the position of solitary wave states in the linear energy band. Our results provide a potential way to adjust the types of solitary waves in BECs with helicoidal gauge potential.

Different types of solitary waves in a thermo-hyperelastic neo-Hookean cylindrical shell

Based on the hyperelastic material models, the propagation of nonlinear travelling waves in cylindrical rods has been studied. Here, different types of nonlinear travelling waves in a thermo-hyperelastic neo-Hookean cylindrical shell are determined. By using the variational principle, a complex differential dynamical system describing the axisymmetric motion of the shell is derived. The effect of the temperature fields is considered. Moreover, the structure is extended from a one-dimensional rod to a three-dimensional cylindrical shell. Then in terms of the bifurcation theory, a detailed qualitative analysis of the system is carried out, and for the bifurcation parameters, their corresponding critical bifurcation values are determined. Combining with the orbits in phase diagrams under different parameters, solitary waves and periodic waves are found in the shell. It is worth pointing out that the solitary waves with the valley form may appear in the radial direction of the shell. The implicit analytical solutions and profiles of these travelling waves are given. There is a promising prospect for the propagation of strongly nonlinear travelling waves to detect structural defects and determine material parameters.

Solitary wave formation under the interplay between spatial inhomogeneity and nonlocality.

The presence of spatial inhomogeneity in a nonlinear medium restricts the formation of solitary waves (SW) on a discrete set of positions, whereas a nonlocal nonlinearity tends to smooth the medium response by averaging over neighboring points. The interplay of these antagonistic effects is studied in terms of SW formation and propagation. Formation dynamics is analyzed under a phase-space approach and analytical conditions for the existence of either discrete families of bright SW or continuous families of kink SW are obtained in terms of Melinikov's method. Propagation dynamics are studied numerically and cases of stable and oscillatory propagation as well as dynamical transformation between different types of SW are shown. The existence of different types and families of SW in the same configuration, under appropriate relations between their spatial width and power with the inhomogeneity and the nonlocality parameters, suggests an advanced functionality of such structures that is quite promising for applications.

From solitons to rogue waves in nonlinear left-handed metamaterials.

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

Painlevé analysis, Lax pair, Bäcklund transformation and multi-soliton solutions for a generalized variable-coefficient KdV–mKdV equation in fluids and plasmas

In this paper, a variable-coefficient non-isospectral Korteweg–de Vries–modified Korteweg–de Vries equation arising in fluids and plasmas is investigated. The integrability of such an equation is studied with Painlevé analysis. Under the integrable condition obtained, the Lax pair is also established through the Ablowitz–Kaup–Newell–Segur procedure. The equation is transformed into its bilinear form by virtue of which the multi-soliton/breather solutions and Bäcklund transformation are derived. Soliton propagation, multi-soliton, soliton–breather and breather–breather interactions are studied: different types of solitary waves can be seen with the change of variable coefficients, the existence of compression or broadening depends on the sign of the non-uniformity coefficient, and during the soliton–breather interaction, the propagating direction of the breather is not influenced by the elevation (positive amplitude) or depression (negative amplitude) soliton.

Propagation of dispersion–nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

In this paper, a generalized nonlinear Schrödinger–Maxwell–Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Bäcklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed.

Comments on “Interactions among different types of solitary waves in (2+1)-dimensional system” by Cheng-lin Bai, Cheng-jie Bai, Hong Zhao [Chaos, Solitons and Fractals 25 (2005) 481

Abstract Starting from a quite universal formula, which is valid for some quite universal (2 + 1)-dimensional physical models, Bai et al. [Bai CL, Bai CJ, Zhao H. Chaos, Solitons & Fractals 2005;25:481] have claimed that the interactions among different types of solitary waves like peakons, dromions, and compactons are investigated both analytically and graphically. We show that all of the claims by Bai et al. are wrong since the adopted q -functions do not satisfy the differential equation. From this point of view, the interactions for peakon–antidromion, compacton–antidromion, and antipeakon–compacton say nothing of completely inelastic or not completely elastic.

Interactions among different types of solitary waves in (2+1)-dimensional system

Abstract Starting from a quite universal formula, which is valid for some quite universal (2 + 1)-dimensional physical models, the interactions among different types of solitary waves like peakons, dromions, and compactons are investigated both analytically and graphically. Some novel features or interesting behaviors are revealed. The results show that the interactions for peakon–antidromion, compacton–antidromion, and antipeakon–compacton may be completely inelastic or not completely elastic.

Interactions among Peakons, Dromions, and Compactons in (2+1)-Dimensional System

Starting from a quite universal formula, which is valid for some quite universal (2+1)-dimensional physical models, the interactions among different types of solitary waves like peakons, dromions, and compactons are investigated both analytically and graphically. Some novel and interesting features are revealed. The results show that the interactions for peakon-dromion, compacton-dromion, and peakon-compacton may be completely inelastic, not-completely elastic or completely elastic. - PACS numbers: 05.45.Yv, 02.30.Jr.

Interactions Among Peakons, Dromions, and Compactons for a (2+1)–Dimensional Soliton Systemy**The project supported by National Natural Science Foundation of China under Grant No. 10172056, the Natural Science Foundation of Zhengjiang Province of China, and the Foundation of Zhengjiang Lishui Normal College under Grant Nos. KZ03009 and KZ03005

Starting from the known variable separation excitations of a (2+1)-dimensional generalized Ablowitz–Kaup–Newell–Segur system, rich coherent structures can be derived. The interactions among different types of solitary waves like peakons, dromions, and compactons are investigated and some novel features or interesting behaviors are revealed. The results show that the interactions for peakon-dromion, compacton-dromion, and peakon-compacton may be completely nonelastic or completely elastic.

Incoherent switching between multistable cavity solitons in a semiconductor optical resonator

We demonstrate numerically a two-dimensional threefold storage scheme based on different types of solitary waves in the transmitted field of a semiconductor planar resonator. Switching between among different solitary waves can be achieved by use of a weak incoherent switching beam.

Kink manifolds in (1+1)-dimensional scalar field theory

The general structure of kink manifolds in (1 + 1)-dimensional complex scalar field theory is described by analysing three special models. New solitary waves are reported. Kink energy sum rules arise between different types of solitary waves.