The freeze of intrapulse Raman scattering effect of ultrashort solitons in optical fiber

The effect of intrapulse Raman scattering (IRS) for the propagation of the femtosecond solitons in an optical fiber is investigated. To factually simulate its influence, a combination of 27 Lorentian lines to fit experimental Raman gain profile is adopted. By using nonlinear Schrödinger equation and finite-difference time domain method, the propagations of femtosecond fundamental solitons in an optical fiber are numerically calculated. When the initial power is suitably enhanced, it is found that the pulse shape is almost the same as initial pulse and the delay Raman response only makes small pulse shift. In other words, when ultrashort soliton is considered, the IRS effect is similarly frozen under the enhanced initial power.     

A HIERARCHY OF INTEGRABLE LATTICE SOLITON EQUATIONS AND ITS INTEGRABLE SYMPLECTIC MAP

1TheLatticeSolitonHierarchyDenoteEf(n)-f(n 1),nEZ,andwritef(n)=f,f(n k)=E*f.Considerthediscrete3x3matrixspectralproblem:whereajb,carethreepotentials,Aisaconstantspectralparameter.Theadjointrepresentationequationof(1)iswhereeachentryVj=Kj(B(A),C(A),D(A))0fthe3x3matrixVisaLaurentexpansionofA:Then(2)isequivaentt0'therecursi0nrelations:\,Theaboverecursionequationscanbesolvedsuccessivelyt0deducethefollowingresults:Wedefine{Dj}bythefollowingrelation:From(3)we0btainKGj-1=JGj,Gj=(Aj,Bj,Cj…     

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using φ-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of φ-mapping. In our solution, the flux of this soliton is naturally quantized.     

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.     

The Application of Mode-Locked Laser Technologies to Long Distance Transmission and Control of Soliton

The control scheme of long distance optical transmission is treated based on conception of mode-locked Laser cavity in this paper. The general mode-locking equation of fiber ring soliton Laser is first constructed, then we give the general perturbed nonlinear schrödinger equation, and finally the transmission and control equations of optical soliton communication systems with various different configurations, respectively, are obtained.     

Deformed soliton,breather,and rogue wave solutions of an inhomogeneous nonlinear Schrdinger equation

We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schro¨dinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schro¨dinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schro¨dinger equation under a suitable parametric condition.     

Effect of polarization on the trajectory of dissipative solitons

We show that the optical Magnus effect for dissipative solitons is determined not only by the helicity but also by the topological index, i.e., by the magnetic quantum number or by the projection of the soliton orbital moment on its trajectory. In the case of inhomogeneous media, we find a relation between the optical Magnus effect and the nonholonomy of the field of unit vectors tangent to the trajectory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 126–134, January, 2009.     

Korteweg-de Vries hierarchy as an asymptotic limit of the Boussinesq system

For the model of surface waves, we perform an asymptotic analysis with respect to a small parameter ε for large times where corrections to the approximation described by the Korteweg-de Vries equation must be taken into account. We reveal the appearance of the Korteweg-de Vries hierarchy, which ensures the construction of an asymptotic representation up to the times t ≈ ε⁻², where the Korteweg-de Vries approximation becomes inapplicable. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 294–304, February, 2008.     

非线性单模光纤中源啁啾孤子相互作用

本文采用分步傅氏变换法对非线性单模光纤中源啁啾孤子相互作用进行了详细的数值研究.所得结果揭示了先源啁啾对孤子相互作用影响的本质,为设计光源啁啾情况下的孤子传转系统提供了依据.