Proton Transport in Hydrogen-Bonded Chains in the Presence of an External Field

The motion of a kink pair consisting of kink soliton in different sublattices in hydrogen-bonded chains in the presence of an external force and damping is discussed based on a new soliton model. The scattering cross-section of a kink pair for an electromagnetic wave and the mobility of a kink pair are found.     

氢键分子系统中外场与阻尼作用下扭结孤子对的特性研究

运用二分量孤子的振子模型,研究了氢键分子系统中在外场与阻尼存在情况下,质子子晶格与重离子子晶格中扭结孤子形成的孤子对的运动特性,讨论了重离子运动对孤子对迁移率的影响和孤子对的核化特性,得到了孤子对迁移率表达式和平均核化率 关键词：     

Two-Component Solitary Waves in Hydrogen-Bonded Molecular Systems

The dynamics of two-component solitary waves in hydrogen-bonded chains in an external force and damping is investigated. The influence of the motion and the optical mode of the heavy ion sublattice on the portion sublattice is discussed. It will increase the soliton width and decrease the soliton mobility. The general expression for the kink soliton soliton is obtained. The velocity, the mobility and conductivity of the kink soliton are calculated. The results are in good agreement with the experimental data.     

Motion of Kink in Hydrogen-Bonded Chain with Asymmetric Double-Well Potential

We discuss the nonlinear excitations and the motion of kink in hydrogen-bonded chain with asymmetric double-well potential, in presence of an external force and damping using a new two-component soliton model. We obtain the kink soliton solution using the phase-plane method, we study soliton velocity and find the expression of the mobility of the kink soliton.     

广义色散Camassa-Holm模型的奇异孤子

引进一类广义色散Camassa-Holm模型，对其做奇异性分析.通过改进的WTC-Kruskal算法，证明该模型在Painlevé意义下可积，得到了它的一组Painlevé-Bcklund系统和Bcklund变换.应用Maple进行代数运算，得到了丰富的规则(regular)孤子和一类奇异(singular)孤子，扭结(kink)孤子,紧孤子(compacton)和反紧孤子(anti-compacton).特别地，推导出一类在扭结孤子的中间区域包含有一列周期尖点(cuspon)波的奇异结构.在这些规则的孤子系统的基础上，对可积广义系统应用Bcklund变换，得到三类奇异孤子，分别是具有驼峰结构的周期爆破波，具有爆破波结构的扭结孤子和紧孤子. 关键词： 广义Camassa-Holm 模型 周期尖点波 紧孤子 周期爆破波     

Spatio-Temporal Deformation of Kink-Breather to the (2+1)-Dimensional Potential Boiti–Leon–Manna–Pempinelli Equation

In the paper, the rational breather soliton and kink solitary wave solution of the (2+1)-dimensional PBLMP equation are obtained by adopting Hirota bilinear method and selecting different test functions. Furthermore, it has been found that the fusion and degeneration of the kink solitary wave occur when interaction between the rational breather soliton and the kink solitary wave happens. These phenomena are very helpful in researching soliton dynamical complexity in the higher dimensional systems.     

Solitons molecules,lump and interaction solutions to a (2+1)-dimensional Sharma–Tasso–Olver–Burgers equation

Different resonance constraints enrich the behavior of soliton solutions. The soliton molecules, which are the bound states of solitons, can be set off by the velocity resonance. The lump waves, which are localized in all directions in space, are theoretically regarded as a limit form of soliton in some ways. In this paper, a (2+1)-dimensional Sharma–Tasso–Olver–Burgers (STOB) equation is investigated. Soliton (kink) molecule, half periodic kink(HPK) and HPK molecule are studied. Then the lump solution is obtained and the interactions between lump and kink molecule are discussed. The kink molecule-lump solutions exhibit a fusion phenomenon and a rogue (instanton) phenomenon, respectively.     

Fission and Fusion of Solitons for the （1＋1）—Dimensional Kupershmidt Equation

By means of the heat conduction equation and the standard truncated Painleve expansion,the (1 1)-dimensional Kupershmidt equation is solved.Some significant exact multi-soliton solutions are given.Especially,for the interaction of the multi-solitons of the Kupershmidt equation,we find that a single(resonant)kink or bell soliton may be fissioned to several kink or bell solitons,Inversely,several kink or bell solitons may also be fused to one kink or bell soliton.     

Kink Pair in Hydrogen Bonded Systems with Symmetric Double-Well Potential

In hydrogen-bonded systems with a symmetric double-well potential, using the variational method, we study the nonlinear excitations and motion of the solitons in the presence of the optical mode of the heavy ion sublattice, based on a new two-component soliton model. We give the equations of motion and soliton-solutions in such a case. Based on these results we calculate further the energy, the momentum and the effective mass of the kink pair.     

Solitons in a deformed ferromagnet with anisotropy of the easy plane type

Soliton dynamics is studied in a compressed ferromagnetic chain having anisotropy of the “easy plane” type. It is shown that there exists a soliton wave of lattice deformation which follows the magnetic soliton. Two models are considered for the connection between deformation and spins. The soliton renormalization constant is found. The effect of lattice anharmonicity is studied.     

Surface defect kink solitons

We reveal the existence of dynamically stable nonlinear defect kink modes at an interface separating a defocusing Kerr medium and an imprinted semi-infinite lattice with a positive or negative defect covering single or several lattice sites. Increasing the number of defect sites equivalently results in a band-gap shift of lattice which in return alters the existence domains and stability properties of defect solitons. Comparing with the uniform semi-infinite lattice, the instability of kink soliton in lattice with a negative defect is significantly suppressed, especially for in-phase soliton. Our results provide an effective way for the realization of stable in-phase kink solitons.     

Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation

Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures.By introducing the velocity resonance mechanism to the multiple kink solutions,we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients.The ...     

The window Josephson junction: a coupled linear nonlinear system

We investigate the interface coupling between the two-dimensional sine-Gordon equation and the two-dimensional wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effective one-dimensional model, and using soliton perturbation theory, compute the fixed points that can trap either a kink or antikink at an interface between two sine-Gordon media. This approximate analysis is validated by comparing with the solution of the partial differential equation and describes kink motion in the one-dimensional window junction. Using this, we analyze steady-state kink motion and derive values for the average speed in the one- and two-dimensional systems. Finally, we show how geometry and the coupling parameters can destabilize kink motion.     

非线性延时修正光纤孤子方程的稳态解问题Ⅰ.静态扭结孤波解

严格求解含非线性延时修正光纤孤立子方程,得到一类完全不同于光纤中已知的亮孤子和暗孤子的新型光学孤波解,并讨论了其物理含义及在光纤实验中观察这种扭结孤波的可能性。     

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in anFPU-β lattice, with the nearest-neighbor interaction and quartic anharmonicity. We get the motion equations of our discrete system by adding noise and damping to the set of deterministic motion equations. We define ``half-time' as the time when the amplitude of the envelope soliton decreases by half due to damping. And then the mass, center and half-time of the perturbed envelope soliton are numerically simulated, beginning with the discrete envelope soliton at rest. Results show successfully how noise affects behavior of the envelope soliton.     

Fine structure of the soliton signal in the magnetic chain in an external magnetic field near a critical value

As is known, there is a critical magnetic field which separates two principally different zones for the soliton signal propagation in magnetic chains, the sine-Gordon zone and the Heisenberg zone. We investigate the fine structure of these signals in a neighborhood of the critical field with nonzero soliton velocity. Explicit formulas both for the azimuthal kink and meridional soliton are obtained. These formulas take into account the nonlinear interaction of soliton structures. Dedicated to the memory of Vladimir Borovikov     

Soliton trapping and repulsion due to a co-group in trans-polyacetylene

For a chain of trans-polyacetylene with one CO substitution the equations of motion of the couples electron phonon system are integrated within the Su-Schrieffer-Heeger model. The calculations for the time-evolution of an end generated kink show that a -C(=O)- unit presents a trap for both a neutral and a negatively charged kink and a repulsive barrier for a positively charged kink. The limitations of the soliton model are discussed.     

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.     

Interaction of Hopping Electrons with Acoustic Phonon and Soliton Excitation in an Inharmonic Linear Chains with Thermal Vibration

With the existence of thermal vibration effect taking in to account, interactions of hopping electrons with lattice acoustic phonon and soliton excitation in inharmonic linear chains are discussed. A new nonlinear equation of probability amplitude for electron motion is obtained. The new results of soliton solution in the form of hyperelliptic integral are obtained as well. It is proved that there exists soliton excitation of kink type in addition to that of bell type found in general.     

Exact Solutions and Coherence Structures of Generalized Breor-Kaup Equations

Using the mapping method based on q-deformed hyperbolic functions, the exact solutions of generalized Breor-Kaup equations are obtained. Based on the solutions, two coherent structures, periodic-branch kink and nonpropagating kink, have been obtained. Moreover, one solitonal interaction form, two line solitons interaction on the kink background, has been found.