General Solution for Hamiltonians with Extended Cubic and Quartic Potentials

In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases 1:6:1 and 1:6:8.     

Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode

We investigate the dynamics of the wave packet formed by two codirected strongly interacting waves propagating in a medium with cubic nonlinearity. We obtain a soliton solution of the nonlinear Schrödinger equation in the degenerate case where the wave packet is described by a single partial momentum. In the nondegenerate case, we use the variational method to find the equation for the pulse duration, which turns out to be analogous to the equation for the coordinate in the Kepler problem. Solving it, we find the dependences of the pulse duration on the propagation distance in the cases of finite and infinite propagation regimes.     

用三角函数法获得非线性Boussinesq方程的广义孤子解

找到一个合适的代换——三角函数法，将非线性Boussinesq微分方程转换为非线性代数方程组.用吴消元法求解该非线性代数方程组，从而获得一般形式Boussinesq微分方程的广义孤子解. 关键词： Boussinesq方程 吴消元法 非线性代数方程组 孤子解     

向列相液晶中强非局域空间光孤子传输的理论研究

对向列相液晶中非局域空间孤子的传输进行了理论研究.基于非线性液晶孤子传输方程，采用Gauss形式的试探解，不仅得到了空间孤子的解析解,而且还在临界功率附近得到了呼吸子的解析解.通过数值模拟证明我们的结果比Conti和Assanto等人的结果更合理.同时，对液晶中的非局域孤子模型和Snyder等提出的强非局域孤子模型进行了全面的比较. 关键词： 向列相液晶 空间孤子 非局域非线性 呼吸子     

强非线性发展方程孤波近似解

研究了一个强非线性发展方程.利用变分原理，首先构造了相应的泛函.选取Lagrange乘子，再用广义变分迭代方法得到了孤波的任意次精度的近似解. 关键词： 发展方程 非线性 孤立子 近似方法     

共振光子晶体中Laue孤子传播的动力学行为

从理论上研究了Laue孤子传播的动力学行为，并通过数值模拟验证了这些行为.结果表明，由于非线性衍射，入射脉冲会分裂产生四种模式，其中产生的Laue孤子的传播行为与一般共振介质中孤子的传播行为相似.     

非线性光学格子中的光束演化研究

研究光学格子中(即在光传输的横截面上存在周期格子势的调制)光束的演化，利用变分原理，求出了光束宽度、振幅、频率啁啾参量随传播距离的演化形式.发现光束宽度与调制周期的比值必须小于一定的值才能形成孤子的传输；同时，还得到了光束在不同的条件下存在着不同的传输过程.光学格子中周期格子的作用有类似非线性的良好的特性，周期格子的引入提供了可以更好地控制格子孤子的形成和传输的参考条件.     

Intra-Channel Collision of Dual-Power Law Optical Solitons

The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are the nonlinear gain and saturable amplifiers along with filters. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the quasi-particle theory. OCIS codes: 060.2310; 060.4510; 060.5530; 190.3270; 190.4370.     

A Generalized Method and Exact Solutions in Bose-Einstein Condensates in an Expulsive Parabolic Potential

In the paper, a generalized sub-equation method is presented to construct some exact analytical solutions of nonlinear partial differential equations. Making use of the method, we present rich exact analytical solutions of the onedimensional nonlinear Schr(o)dinger equation which describes the dynamics of solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential. The solutions obtained include not only non-traveling wave and coefficient function's soliton solutions, but also Jacobi elliptic function solutions and Weierstrass elliptic function solutions. Some plots are given to demonstrate the properties of some exact solutions under the Feshbachmanaged nonlinear coefficient and the hyperbolic secant function coefficient.     

梯度折射率非局域介质中空间孤子振荡行为研究

应用等效粒子近似方法研究了光学空间孤子在带有局域和非局域非线性横向非均匀介质中的传输动力学行为.发现孤子在传播过程中横向的周期性振荡.折射率调制幅度和波导的归一化宽度决定了振荡周期的大小.介质的非局域对振荡振幅有着较小的影响.模拟了孤子传输过程,所得数值结果与理论分析符合很好.此外,模拟传输还发现多孤子束缚态能够在这个模型中稳定传播.这种振荡特性或许可以应用于光学路由器、转换器、开关等.