Strange solitons in a chiral quark-meson model

We consider aSU(3) quark soliton model based on chiral invariant quark-meson coupling. We find soliton solutions with nonzero strangeness andB=1 in the model with nontrivial kaonic fields, for values of the coupling constant greater than the phenomenologically acceptable number. Hence they do not correspond to known strange baryons.     

Control and characterization of spatio-temporal disorder in parametrically excited surface waves

The nonlinear interactions of parametrically excited surface waves have been shown to yield a rich family of nonlinear states. When the system is driven by two commensurate frequencies, a variety of interesting superlattice type states are generated via a number of different 3-wave resonant interactions. These states occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two different unstable modes generated by the two forcing frequencies. Near the system’s bicritical point, a well-defined region of phase space exists in which a highly disordered state, both in space and time, is observed. We first show that this state results from the competition between two distinct nonlinear super-lattice states, each with different characteristic temporal and spatial symmetries. After characterizing the type of spatio-temporal disorder that is embodied in this disordered state, we will demonstrate that it can be controlled. Control to either of its neighboring nonlinear states is achieved by the application of a small-amplitude excitation at a third frequency, where the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency used. This technique can also excite rapid switching between different nonlinear states.     

光纤中短间距脉冲串的非线性传输特性与混沌孤子波包产生

采用分步傅里叶算法,在基元脉冲数分别为9、17和25及相邻基元脉冲时间间隔分别为1、2及3的情况下,对短间隔脉冲串在光纤负色散区的非线性传榆特性进行数值研究.研究结果表明,尽管脉冲数、脉冲位置、脉冲强度和相邻两脉冲间的时间间隔随距离变化,且在传输过程中弱脉冲基座会扩展到很宽的时间范围,但是整个主脉冲波包始终保持局域即其时间间隔几乎不变,展宽速度不明显.同时,主脉冲波包永不重复前面的轮廓,即波包演化出现混沌行为.短间隔脉冲串的非线性演化可以形成混沌孤子波包,基元脉冲间的时间间隔及脉冲串的脉冲数都会影响混沌孤子波包的子脉冲数和它的持续时间.     

基于非线性放大环镜和Lyot滤波器的多波长与耗散孤子锁模态开关型掺铥光纤激光器

报道了一种基于非线性放大环镜和Lyot滤波器技术的态开关型掺铥光纤激光器.通过仔细调节偏振控制器和泵浦功率,掺铥光纤激光器可以分别在多波长态和耗散孤子锁模态运行,并且两种态之间可以相互切换.对于多波长态,在光谱半功率值范围内能生成8个稳定的波长;对于耗散孤子锁模态,在1996 nm的中心波长处产生脉冲能量高达41.49 nJ,脉冲持续时间为2.4 ns,光谱带宽为29 nm的耗散孤子.不同运行态间的切换归因于偏振控制器导致的非线性放大环镜的功能的改变.     

Nonlinear dynamics: Challenges and perspectives

The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.     

Soliton and other solutions to the (1+2)-dimensional chiral nonlinear Schrödinger equation

The (1+2)-dimensional chiral nonlinear Schrödinger equation (2D-CNLSE) as a nonlinear evolution equation is considered and studied in a detailed manner. To this end, a complex transform is firstly adopted to arrive at the real and imaginary parts of the model, and then, the modified Jacobi elliptic expansion method is formally utilized to derive soliton and other solutions of the 2D-CNLSE. The exact solutions presented in this paper can be classified as topological and nontopological solitons as well as Jacobi elliptic function solutions.     

Nonlinear Kac model: Spatially homogeneous solutions and the Tjon effect

We study Kac's nonlinear model of the Boltzmann equation when the cross section() does not satisfy the special symmetry condition()=(-). We determine a differential system for the Laguerre moments of the odd and even velocity parts of the solutions. We consider the spatially homogeneous model in 1+1 dimensions (velocityv and timet) when the even velocity part of the solution is provided by the Bobylev-Krook-Wu closed solutions and study the associated odd velocity part. We find that the solutions depend on the microscopic models of(). For one class of(), which has sums of exponential terms for the Laguerre moments, we establish the relations allowing the construction of the time-dependent solutions associated with any initial distribution. We find sufficient conditions on() and on the even part such that the Laguerre series of the odd part converges. We establish a criterion for a well-defined linear combination of the moments cross section, and we check its validity for different numerical examples. We find that if the relaxation time for the even part is smaller than the corresponding one for the odd part and if the initial distribution has a narrow peak, then the Tjon effect exists for the complete B.K.W. solution (even+odd parts).     

Bistable behaviour in squeezed vacua: II. Stability analysis and chaos

Linear stability analysis and (numerical) investigation of the periodic and chaotic self-pulsing behaviour are presented for the Maxwell-Bloch equations of a bistable model in contact with a squeezed vacuum field. Effect of the squeeze phase parameter on the period doubling bifurcation that preceeds chaos is examined for the adiabatic and non-adiabatic regimes.     

Stochastic and coherence resonance in lasers: homoclinic chaos and polarization bistability

We report Stochastic Resonance and Coherence Resonance phenomena in experiments using CO₂ lasers. First, we consider a polarized laser with feedback; for suitable feedback parameters, the laser intensity undergoes homoclinic chaos consisting in the return to a saddle focus, where noise controls the permanence time around the saddle. Second, we discuss a quasi-isotropic laser where noise induces switching between two intensity components with mutually orthogonal polarization.     

Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model

The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general features of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of pump and probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response functions cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kr?nig relations for the two lowest moments of the real and of the imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analytic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model dependent and therefore have a general validity, provided one substitutes for the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators. Received 25 January 1999 and Received in final form 26 April 1999