Soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m, n) equations

We consider the nonlinear dispersive K(m,n) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sech^p function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m,n) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K(m,n) equations in the presence of the generalized evolution term. An extended form of the K(m,n) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K(m,n) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients.     

1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity

This paper obtains the 1-soliton solution of the Jaulent-Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler-Lagrange operator annihilates the total divergence.     

化学中的孤子

本文根据有机导电材料的基本特征,从化学的角度讨论了孤子、极化子的产生、结构和性质。对其它化学体系中的孤子和极化子模型做了简单介绍。     

高分子链通过机械化学反应的信息、能量协同激发实现化学能直接转换为机械能研究的新进展

机械化学反应是指将化学能与机械能直接相互转换的过程。由于机械化学反应可将化学能和机械能直接相互转换,并且有无污染、无噪音、无废物排放和能量转换高等特点,因而正日趋受到世界各国,尤其是发达国家的关注。信息文明的时代一定会有与之相应的物质和能量与信息状态的转换相伴,掌握信息和使用信息是这个时代发展的必然要求。为此,作者通过对高分子物质激发态的分析,从物质、能量和信息三者协同的角度对机械化学反应的原理进行了探讨,并试图用孤子激发来阐明化学能和机械能相互直接转换的原因。随着高分子合成技术的不断发展,我们有可能通过用机械化学反应的手段来为信息文明的时代找到并提供一种新的能源和能量转换方式,并且有可能会导致新的产业革命。     

色散缓变光纤中皮秒孤子脉冲的压缩

本文实验研究了孤子脉冲在色散缓变光纤中传输时的动力学特性,发现孤子脉冲在色散缓变光纤中能被压缩.采用500米色散缓变光纤,成功将4.4ps的孤子脉冲压缩到830fs,脉冲压缩比为5.3.色散缓变光纤中孤子脉冲压缩的实验研究为超短光脉冲压缩提供了新的途径和方法.     

A (1+1)-dimensional integrable system with fifth order spectral problems and four dispersion relations

A new (1+1)-dimensional integrable model is investigated, of which the Lax integrability is shown by the existence of its fifth order spectral problems. Its bilinear form is obtained via introducing an auxiliary variable. The multiple soliton solutions are obtained by solving its bilinear system. It is shown that there are four different dispersion relations for multiple solitons. The amplitudes of the solitons are only wave number dependent while the velocities of the solitons are not only wave number dependent but also dispersion relation dependent. Because of the existence of four dispersion relations, the interactions among solitons are much more abundant because for any fixed wave number there are four different velocities including two left moving and two right moving. Especially, the existence of the multiple velocities makes the velocity resonant conditions can be readily satisfied to form many types of bound states including soliton molecules, soliton-breather molecules and breather molecules.     

Perturbed soliton excitations in the DNA double helix

We study the nonlinear dynamics of the inhomogeneous DNA double-helical chain using the dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation, while taking into account the interstrand hydrogen bonding energy, between bases, and the intrastrand inhomogeneous stacking energy and by making an analogy with the Heisenberg model of the Hamiltonian of an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagnetic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of an open state configuration in the DNA double helix. The effect of inhomogeneity in the stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple-scale soliton perturbation theory by solving the associated linear eigenvalue problem and by constructing the complete set of eigenfunctions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of the inhomogeneity. Also it introduces fluctuations in the form of a train of pulses or periodic oscillations in the open state configuration.     

Soliton Lattice and Gas in Passive Fiber-Ring Resonators

We consider multisoliton patterns in the model of a synchronously pumped fiber-loop resonator. An essential difference of this system from its long-line counterpart is that, due to the finite length, dynamical regimes may be observed that would be unstable in the infinitely long line. For the case when the effective instability gain, produced by competition of the modulational instability (MI) of the flat background and losses, is small, we have consistently derived a special form of the complex Ginzburg-Landau equation for a perturbation above the continuous wave (cw) background. It predicts bound states of pulses with a uniquely determined ratio of the pulse width to the separation between them. Direct numerical simulations have produced regular soliton lattices at small values of the feeding pulse power, and irregular patterns at larger powers. Evidence for a phase transition between the lattice and gas phases in the model is found numerically. At low power, the width-to-sep aration ratio as found numerically proves to be quite close to the analytically predicted value. We also compare our results with recently published experimental observations of MI-stimulated formation of a pulse array in a mode-locked fiber laser.