二阶孤子间相互作用引起孤子衰变

对于二阶孤子脉冲对,通过数值求解非线性Schrdinger方程,得到了二阶孤子在光纤中传输时的衰变规律.由于脉冲之间的相互作用,原来的二阶孤子衰变为两个分离的基孤子.二阶孤子对同位相时,相互作用为“吸引”,衰变后峰值小的基孤子位于内侧,二阶孤子对反位相时,相互作用为“排斥”,衰变后峰值小的基孤子位于外侧.两个二阶孤子脉冲间隔越小,反位相时,在相同传输距离处,衰变产生的两个基孤子的分离程度越大.     

Quartic B-spline Galerkin approach to the numerical solution of the KdVB equation

The nonlinear Korteweg-de Vries–Burgers’ equation is solved numerically by method of Galerkin using quartic B-splines as both shape and weight functions over the finite intervals. Five test problems are studied to demonstrate the accuracy and efficiency of the proposed method. A comparison of numerical results of both algorithm and some published articles is done in computational section. The numerical results are found in good agreement with exact solutions.     

Bilinear Bäcklund transformation and Lax pair for a coupled Ramani equation

In this paper, a coupled Ramani equation is proposed. The bilinear Bäcklund transformation and Lax pair for this equation are derived starting from its bilinear form. Multisoliton solutions to the system can also be obtained.     

New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions

In this paper, by the Darboux transformation together with the Wronskian technique, we construct new double Wronskian solutions for the Whitham-Broer-Kaup (WBK) system. Some new determinant identities are developed in the verification of the solutions. Based on analyzing the asymptotic behavior of new double Wronskian functions as t → ±∞, we make a complete characterization of asymptotic solitons for the non-singular, non-trivial and irreducible soliton solutions. It turns out that the solutions are the linear superposition of two fully-resonant multi-soliton configurations, in each of which the amplitudes, velocities and numbers of asymptotic solitons are in general not equal as t → ±∞. To illustrate, we present the figures for several examples of soliton interactions occurring in the WBK system.     

The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory

Recently we have reported on the existence of finite energy SU(2) Yang–Mills–Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft–Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft–Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z$z$-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z$z$-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ$\lambda$. However the dipole separation and the magnetic dipole moment decrease with λ$\lambda$. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.     

Interaction of solitary waves for the generalized KdV equation

We consider a class of generalized KdV equations with a small parameter and nonlinearities of the type u^m. We create a finite differences scheme to simulate the solution of the Cauchy problem and present some numerical results for the problem of the solitary waves interaction. In particular, we consider sufficient condition under which pairs of solitary waves interact, in the asymptotic sense, in accordance with the soliton scenario.     

The integrability and parametric representation of a hierarchy of soliton equations

In this paper after having obtained the Lax pair of a hierarchy of soliton equations,we discuss the parametric representation for finite-band solutions of the stationary solitonequation, and prove it can be represented as a Hamiltonian system which is integrable inLiouville sense. The nonconfocal involutive integral representations {Fm} are obtained also.In the condition of finite-band solutions of the soliton equation, the time and space can bedevided inio two Hamiltonian systems, so the fi…     

负折射介质中可控自陡峭效应对孤子传输的影响

研究了具有非线性极化的负折射介质中孤子脉冲的传输特性,着重分析了在常规非线性传输模型中不曾出现的由负折射介质色散磁导率导致的可控自陡峭效应对孤子传输的影响.结果表明,与正自陡峭效应一样,负自陡峭效应同样造成孤子脉冲的非对称、中心偏移和高阶孤子衰减,但脉冲偏移的方向与正自陡峭效应情形相反.此外,利用可控自陡峭效应可以从某种程度上抵消三阶色散效应导致的孤子脉冲偏移,从而实现孤子脉冲中心的无偏移传输.     

Soliton solutions to the Novikov equation and a negative flow of the Novikov hierarchy

The Novikov equation and a negative flow of the Novikov hierarchy are related to a negative flow of the Sawada–Kotera hierarchy and the Sawada–Kotera equation by reciprocal transformations, respectively. With the help of the Darboux transformations for the negative flow of the Sawada–Kotera hierarchy, the Sawada–Kotera equation and reciprocal transformations, we obtain a parametric representation for $N$-soliton solutions to the Novikov equation and the negative flow of the Novikov hierarchy.     

On the cross curvature flow

In this paper, we study the cross curvature soliton. We study the cross curvature soliton with a warped product structure. On the other hand, we show that the volume entropy is decreasing along the cross curvature flow.