具有双曲正割型折射率的线性和非线性介质中的光呼吸子

通过数值模拟研究具有横向双曲正割型折射率调制的线性和非线性介质中光的传输。结果显示光束在传输过程中有呼吸的特性,其呼吸周期可以通过折射率调制的深度和宽度加以改变。同时讨论具有不同初始相位的两相邻光束之间的相互作用。指出周期性在初始相位相同时出现,在初始相位相反时可以通过适当地选择光束间距形成束缚态。     

Predicting eddy detachment for an equivalent barotropic thin jet

Summary The time-dependent meandering of thin ocean jets in reduced gravity models has recently been shown to obey a natural coordinate version of the standard modified Korteweg-deVries (mKdV) equation. The detachment of eddies from such a jet begins when different segments of the jet path come into contact, causing the initially simply connected jet to “pinch” together. It is shown that this pinching process is effected primarily by breather solutions to the mKdV equation. For a given initial condition the solution will evolve into a dispersive wave train plus a finite number of breathers, the connectivity of which is determined by a steepness parameter λ. Using the scattering transform for the mKdV equation the value(s) of λ can be calculated in a straightforward manner, and the detachment (or lack thereof) of meanders can be forecast to a high degree of confidence by calculating λ. Examples with simple meander disturbances show a remarkable degree of stability and resistance to detachment.     

Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness

Based on the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method, this paper presents the vibration behavior of an isotropic and orthotropic oval cylindrical shell with parabolically varying thickness along its circumference. The governing equations of motion of the shell, which have variable coefficients are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling, which comes from variable curvature and thickness of shell. The vibration equations of the shell are reduced to eight first‐order differential equations in the circumferential coordinate and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for the symmetrical and antisymmetrical modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the shell geometry, ovality parameter, thickness ratio, and orthotropic parameters corresponding to different type modes of vibration is investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

Symmetric and antisymmetric vector solitons for the fractional quadric-cubic coupled nonlinear Schrödinger equation

The fractional quadric-cubic coupled nonlinear Schrödinger equation is concerned, and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method. The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated. Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index, respectively. The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied. Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.     

椭圆响应强非局域非线性介质中的二维异步分数傅里叶变换及光束传输特性

研究了椭圆响应强非局域非线性介质中的光束传输问题. 结果表明:任意光束在这类介质中传输时均遵守二维异步分数傅里叶变换的传输规律. 基于二维异步分数傅里叶变换这一数学工具, 可很方便地对光束的传输进行解析求解并分析其性质. 利用二维异步分数傅里叶变换的性质, 讨论了一般光束的传输性质; 分析了孤子和二维异步呼吸子的形成条件; 得出了孤子/呼吸子的相互作用规律. 关键词： 椭圆响应 强非局域非线性 孤子 呼吸子     

The short pulse equation: Bäcklund transformations and applications

A Bäcklund transformation (BT), which involves both independent and dependent variables, is established and studied for the short pulse (SP) equation. Based it, the nonlinear superposition formulae for 2-, 3-, and 4-BT are presented. The general result for the composition of -BTs is achieved and given in terms of determinants. As applications, various solutions including loop solitons, breather solutions, and their interaction solutions are worked out.     

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

We discuss the geometric characterization of the trajectory of a moving charged particle, for the case of a homogeneous electromagnetic field, in Minkowski space when the motion is governed by the Lorentz equation. We employ a totally relativistic approach during the discussion. It is based on a systematic use of the Faraday antisymmetric tensor properties of the electromagnetic field and of the four‐dimensional Frenet‐Serret formula, which is adapted to the Minkowski 4‐space with index two to determine the worldline geometry of the electromagnetic field acting on the particle. Finally, we present the necessary and sufficient conditions to obtain uniform motion of the relativistic charged particle in a homogeneous electromagnetic field in      

Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather

The Peregrine breather of order eleven(P_(11) breather) solution to the focusing one-dimensional nonlinear Schrdinger equation(NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P_(11) breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the(x; t) plane, in function of the different parameters.     

Integrability Test and Spatiotemporal Feature of Breather-Wave to the (2+1)-Dimensional Boussinesq Equation

Painlev integrability has been tested for (2+1)D Boussinesq equation with disturbance term using the standard WTC approach after introducing the Kruskai's simplification. New breather solitary solutions depending on constant equilibrium solution are obtained by using Extended Homoclinic Test Method. Moreover, the spatiotemporal feature of breather solitary wave is exhibited.     

New Homoclinic and Heteroclinic Solutions for Zakharov System

A new type of homoclinic and heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanical feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlinear evolution system. Moreover, the similarities and differences between homoclinic (heteroclinic) breather and homoclinic (heteroclinic) tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.