Hui-Ling Zhen

Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma

For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.

Dynamic behavior of the quantum Zakharov-Kuznetsov equations in dense quantum magnetoplasmas

Quantum Zakharov-Kuznetsov (qZK) equation is found in a dense quantum magnetoplasma. Via the spectral analysis, we investigate the Hamiltonian and periodicity of the qZK equation. Using the Hirota method, we obtain the bilinear forms and N-soliton solutions. Asymptotic analysis on the two-soliton solutions shows that the soliton interaction is elastic. Figures are plotted to reveal the propagation characteristics and interaction between the two solitons. We find that the one soliton has a single peak and its amplitude is positively related to He, while the two solitons are parallel when He < 2, otherwise, the one soliton has two peaks and the two solitons interact with each other. Hereby, He is proportional to the ratio of the strength of magnetic field to the electronic Fermi temperature. External periodic force on the qZK equation yields the chaotic motions. Through some phase projections, the process from a sequence of the quasi-period doubling to chaos can be observed. The chaotic behavior is observed...

Soliton solutions and chaotic motion of the extended Zakharov-Kuznetsov equations in a magnetized two-ion-temperature dusty plasma

The extended Zakharov-Kuznetsov (eZK) equation for the magnetized two-ion-temperature dusty plasma is studied in this paper. With the help of Hirota method, bilinear forms and N-soliton solutions are given, and soliton propagation is graphically analyzed. We find that the soliton amplitude is positively related to the nonlinear coefficient A, while inversely related to the dispersion coefficients B and C. We obtain that the soliton amplitude will increase with the mass of the jth dust grain and the average charge number residing on the dust grain decreased, but the soliton amplitude will increase with the equilibrium number density of the jth dust grain increased. Upon the introduction of the periodic external forcing term, both the weak and developed chaotic motions can occur. Difference between the two chaotic motions roots in the inequality between the nonlinear coefficient l2 and perturbed term h1. The developed chaos can be weakened with B or C decreased and A increased. Periodic motion of the pertur...

Analytic study on solitons in gas-filled hollow-core photonic crystal fibers

An analytic study on controlling the soliton dynamics in the gas-filled hollow-core photonic crystal fibers is presented in this paper. The bilinear method with the auxiliary function is introduced to derive the bilinear forms for the nonlinear Schrodinger equation. With symbolic computation, the analytic soliton solutions are obtained, and the features and properties of solitons are discussed. The influence of the parameters for the soliton solutions obtained are analyzed. The presented results could be used in soliton control in the gas-filled hollow-core photonic crystal fibers.

Bright optical solitons or light bullets for a (3 + 1)-dimensional generalized nonlinear Schrödinger equation with the distributed coefficients

Under investigation in this paper is a (3 + 1)-dimensional generalized nonlinear Schrodinger equation with the distributed coefficients for the spatiotemporal optical solitons or light bullets. Through the symbolic computation and Hirota method, one- and two-soliton solutions are derived. We also present the Backlund transformation, through which we derive the soliton solutions. When the gain/loss coefficient is the monotonically decreasing function for the propagation coordinate z, amplitude for the spatiotemporal optical soliton or light bullet decreases along z, while when the gain/loss coefficient is the monotonically increasing function for z, amplitude for the spatiotemporal optical soliton or light bullet increases along z. Directions of the solitons are different because the signs of imaginary parts of the frequencies are adverse. Based on the two-soliton solutions, elastic and inelastic collisions between the two spatiotemporal optical solitons or light bullets are derived under different conditions presented in the paper.

Solitons, bilinear Bäcklund transformations and conservation laws for a -dimensional Bogoyavlenskii-Kadontsev-Petviashili equation in a fluid, plasma or ferromagnetic thin film

Abstract In this paper, we investigate a -dimensional Bogoyavlenskii–Kadontsev–Petviashili equation in a fluid, plasma or ferromagnetic thin film. Through the Bell polynomials, Hirota method and symbolic computation, the one- and two-kink-soliton solutions are derived. Bäcklund transformation, Lax pair and conservation laws are presented. Elastic collisions including the oblique, parallel, unidirectional and bidirectional collisions between the two-kink solitons are discussed. In addition, the relation between the velocities and wave numbers of the two-kink solitons are analysed. When wave numbers , the velocities in the x axis, increase with wave numbers increasing. With increasing, increase when , while decrease when . , the velocities in the y axis, increase with increasing and decreasing.

Analytic study on certain solitons in an erbium-doped optical fibre

Abstract ()-dimensional non-linear optical waves through the coherently excited resonant medium doped with the erbium atoms can be described by a -dimensional non-linear Schrödinger equation coupled with the self-induced transparency equations. For such a system, via the Hirota method and symbolic computation, linear forms, one-, two- and N-soliton solutions are obtained. Asymptotic analysis is conducted and suggests that the interaction between the two solitons is elastic. Bright solitons are obtained for the fields E and P, while the dark ones for the field N, with E as the electric field, P as the polarization in the resonant medium induced by the electric field, and N as the population inversion profile of the dopant atoms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons are seen. Influence of the averaged natural frequency on the solitons are studied: (1) can affect the velocities of all the solitons; (2) Amplitudes of the solitons for the fields P and N increase with decreasing, and decrease with increasing; (3) With decreasing, for the fields P and N, one-peak one soliton turns into the two-peak one, as well as interaction type changes from the interaction between two one-peak ones to that between a one-peak one and a two-peak one; (4) For the field E, influence of on the solitons cannot be found. The results of this paper might be of potential applications in the design of optical communication systems which can produce the bright and dark solitons simultaneously.

Solitons and chaos of the Klein-Gordon-Zakharov system in a high-frequency plasma

In this paper, we study the Klein-Gordon-Zakharov (KGZ) system, which describes the interaction between the Langmuir wave and ion sound wave in a high-frequency plasma. By means of the Hirota method and symbolic computation, bright and mixed-type soliton solutions are obtained. For the one soliton, amplitude of E is positively related to β2, and that of n is inversely related to β2, while they are both positively related to α, where E refers to the high-frequency part of the electrostatic potential of the electric field raised by the electrons, and n represents the deviation of ion density from its equilibrium, β2 and α are the plasma frequency and ion sound speed, respectively. Head-on interactions between the two bright solitons and two mixed-type ones are respectively displayed. With β2 increasing, the head-on interaction is transformed into an overtaking one. Bright bound-state solitons are investigated, and the interaction period decreases with α increasing. Furthermore, with the external forces Γ1(t...

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of , but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, and are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.

Dynamics of the Zakharov-Kuznetsov-Burgers equations in dusty plasmas

In this paper, we investigate the Zakharov-Kuznetsov-Burgers (ZKB) equations for the dust-ion-acoustic waves in dusty plasmas. Shock-like and soliton solutions are both constructed through the introduction of an auxiliary function and variable. ZKB-soliton propagation is plotted, and from those figures, we find that energy of the solitons increases when the number of electrons in a dust particle decreases or the mass of such dust particle becomes larger. Considering the external perturbations in the dusty plasmas, we study the perturbed ZKB equation via some qualitative and quantitative methods. To corroborate that the perturbed ZKB equation can indeed give rise to the chaos, we make use of the power spectrum and Lyapunov exponents. Then, we investigate the phase projections, and find that both the weak and developed chaos can be observed. Weak chaos occur when the absolute value of damped coefficient (l1) is stronger than the strength of perturbed term (g1), or else, the developed one occurs. Ranges of l...