Nonlinear Waves in Two-Dimensional (2D) Square Lattice Frenkel-Kontorova (FK) System

A 2D 平方格子被学习。由使用连续统近似，我们在使遭到到一个外部周期的底层潜力的方形的格子为一个任意的粒子建立了运动的微分方程。系统的准确独居的波浪被作出对有利的裁决特殊情况。我们断定粘合剂力量 f 和上面、更低的层的角度 αbetween 繁殖方向能影响这些波浪。

Experiments on the interactions between impurities and solitary waves in lattice model

The interactions between solitary waves and impurities have been studied experimentally in a 1D nonlinear coupled pendulum chain under vertical excitation. The mass and the coupling are unique, except a single pendulum with length impurity in the chain. The experiment reveals: the long impurity repels breather and attracts kink while the short one attracts breather and repels kink under higher frequency driving, and the long impurity attracts breather and repels kink while the short one repels breather and attracts kink under the lower frequency driving. These results prove the current theoretical prediction based on continuum-limit approximation.

非对称相互作用势对孤波散射过程中相移的影响

研究了一维广义FPU-αβ晶格模型中微观粒子之间相互作用势的非对称性对孤波散射过程产生相移的影响,该系统存在两种拓扑孤波,Kink和Antikink。数值计算结果表明:随着非对称性强度增加,同种孤波散射所产生的相移减小,而异种孤波散射所产生的相移增大。为解释上述计算结果,在特殊孤波碰撞位形下将广义FPU-αβ晶格模型近似成具有非线性相互作用的两粒子系统,通过求解两粒子系统的动力学方程发现:在总能量确定的情况下,两粒子最大相对位移的绝对值随非对称性增加而减小;最大相对位移在扣除微观粒子两平衡位置间距后所得到的结果与数值计算得到孤波相移结果一致。