电磁场在超晶中传播的孤子解

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用非线性薛定谔方程讨论超晶格中畴的运动

用非线性薛定谔方程讨论超晶格畴的形成和漂移,得到具有负微分电导特性的超晶格中畴的波函数是Bloch函数的一个孤子型包络函数,它在外电场作用下做漂移运动. 关键词：     

Interaction of kink-lattice solitons with small-amplitude waves in finite-size superlattices

Propagation of large-amplitude electromagnetic fields and their interactions with small-amplitude waves in finite superlattices are considered in the framework of the sine-Gordon theory. Finite-size effects result in modulating the large-amplitude fields to a lattice of kinked waves. This kink-lattice wave displays both a soliton feature and the particle property typical to nonlinear topological excitations. The interaction of the kink-lattice soliton with weak electromagnetic waves reveals an unusual number (exactly three) of bound states, which is attributed to the finite size of the propagation medium.     

Darboux transformation and exact multisolitons for a matrix coupled dispersionless system

We present a matrix coupled dispersionless(CD) system. A Lax pair for the matrix CD system is proposed and Darboux transformation is constructed on the solutions of the matrix CD system and the associated Lax pair. We express an N soliton formula for the solutions of the matrix CD system in terms of quasideterminants. By using properties of the quasideterminants, we obtain some exact solutions, including bright and dark-type solitons, rogue wave and breather solutions of the matrix CD system. Furthermore, it has been shown that the solutions of the matrix CD system are expressed in terms of solutions to the usual CD system, sine-Gordon equation and Maxwell-Bloch system.     

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.     

Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneities

We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electromagnetic waves are governed by the Landau–Lifshitz–Maxwell (LLM) equation, a certain coupling between the Landau–Lifshitz and Maxwell's equations. In the framework of multiscale analysis, we obtain the perturbed integral modified KdV (PIMKdV) equation. Since the dynamic is governed by the nonlinear integro-differential equation, we rely on numerical simulations to study the interaction of its mKdV solitons with various types of inhomogeneities. Apart from simple one soliton experiments with periodic or localised inhomogeneities, the numerical simulations revealed an interesting dynamical scenario where the collision of two solitons on a localised inhomogeneity create a bound state which then produces either two separated solitons or a mKdV breather.     

Dynamics of ultimately short electromagnetic pulses in chiral carbon nanotubes

The wave equation for the electromagnetic field propagating in chiral carbon nanotubes has been analyzed. The phenomenological equation similar to the sine-Gordon equation has been derived. The dynamics of the electromagnetic pulse has been investigated.     

The sine-gordon breather as a moving oscillator in the sense of de broglie

The breather solution of the sine-Gordon equation represents an extended oscillator moving as a whole with constant velocity. We investigate the properties of the breather solution in the context of de Broglie's basic concept of “moving oscillator”, which led to quantum mechanics. We show that the momentum of the breather is proportional to its wave vector, and its total energy is proportional to the oscillator frequency.     

New class of extremely short electromagnetic solitons

A physical realization is presented for the integrable modified sine-Gordon equation. In this case, this equation describes the propagation of an extremely short vector electromagnetic pulse in the system of asymmetric quantum objects that have permanent dipole moments in the self-energy states. Using soliton solutions for ordinary and extraordinary components, new regimes of the dynamics of the pulse and medium that are specific only to asymmetric media have been found.     

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.     

Kink degeneracy and rogue potential solution for the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

In this paper, we obtained the exact breather-type kink soliton and breather-type periodic soliton solutions for the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation using the extended homoclinic test technique. Some new nonlinear phenomena, such as kink and periodic degeneracies, are investigated. Using the homoclinic breather limit method, some new rational breather solutions are found as well. Meanwhile, we also obtained the rational potential solution which is found to be just a rogue wave. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.     

Various Types of Kink and Bright Resonant Soliton Solutions for the (2+1)-Dimensional Double sine-Gordon Equation

The algebraic mapping relations between the (2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein—Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, "V" shape, "snake" shape and "M" shape solitary waves, Zigzag-curve type, "ω" shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions.     

Two-dimensional electromagnetic breathers in an array of nanotubes with multilevel impurities

The propagation of a two-dimensional bipolar electromagnetic pulse in an array of semiconductor carbon nanotubes with multilevel impurities is studied. The electromagnetic field in the array of nanotubes is described by Maxwell’s equations reduced to a non-one-dimensional wave equation. The numerical solution to the wave equation demonstrates the possibility of the propagation of a two-dimensional electromagnetic breather in the array of nanotubes. The character of the evolution of the shape of the breather is elucidated, and the time dependence of the maximum intensity of its field is obtained. It is demonstrated that the introduction of multilevel impurities causes a significant change in the parameters, thereby providing an additional possibility for the stabilization of a laser pulse propagating in an array of semiconducting carbon nanotubes.     

Hirota方程的怪波解及其传输特性研究

求出了高阶Hirota方程在可积条件下的一种精确呼吸子解,并基于此呼吸子解得到了Hirota方程的一种怪波解.在此怪波解的基础上研究了怪波的激发,发现对平面波进行周期性扰动可以激发怪波,对平面波进行高斯扰动可以更快地激发怪波,还可以直接在常数项上增加高斯扰动激发怪波.作为一个实例,采用分步傅里叶方法数值研究了在考虑自频移和拉曼增益时怪波的传输特性,自频移使怪波中心发生偏移,拉曼增益使得怪波分裂得更快,而且拉曼增益值越大怪波分裂得越快,但是拉曼增益对怪波的峰值强度没有明显影响.最后数值模拟了相邻怪波之间的相互作用特点,随着怪波之间距离的减小,怪波将合二为一,成为一束怪波,之后再分裂,并分析了拉曼增益和自频移对怪波相互作用的影响.     

Novel localized wave solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Based on a special transformation that we introduce, the N-soliton solution of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is constructed. By applying the long wave limit and restricting certain conjugation conditions to the related solitons, some novel localized wave solutions are obtained, which contain higher-order breathers and lumps as well as their interactions. In particular, by choosing appropriate parameters involved in the N-solitons, two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution. Five solutions including two breathers, two lumps, and interaction solutions between one breather and two bell-shaped solitons, one breather and one lump, or one lump and two bell-shaped solitons are constructed from the 4-soliton solution. Five interaction solutions mixed by one breather/lump and three bell-shaped solitons, two breathers/lumps and a bell-shaped soliton, as well as mixing with one lump, one breather and a bell-shaped soliton are constructed from the 5-soliton solution. To study the behaviors that the obtained interaction solutions may have, we present some illustrative numerical simulations, which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties. The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations. The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.     

Breather and double-pole solutions for the Benjamin-Ono equation in a stratified fluid

The Benjamin–Ono equation is hereby investigated, which arises in the context of long internal gravity waves in a stratified fluid. With the Hirota method and symbolic computation, breather solutions are derived. Propagation of the breather and elastic collisions between the breather and soliton are graphically analyzed. The collision period and the bunch number in a wave packet are relevant to the ratio of the real part to the imaginary of the wavenumber. Through the coalescence of wavenumbers in the two-soliton solutions, we obtain the double-pole solutions.     

Solitons in superlattices: A tight-binding approach

We present a tight-binding approach of the soliton formations and propagations in superlattices. Negative differential conductivity in superlattices leads to the growth of the inevitable spatial fluctuations and formation of the electron accumulation-layer domain. Based on the negative differential conductivity, it is shown that the envelope of the tight-binding-approach wave functions is governed by the nonlinear Schrödinger equation which has soliton solutions, the result of which suggests soliton formations and propagations in the superlattices.