FPU晶格中对向传播的双孤子解
Counterpropagating Two-Soliton Solutions in the FPU Lattice
摘要：
研究了具有一般最近邻相互作用势的Fermi-Pasta-Ulam模型中小振幅长波长孤波的相互作用。我们建立了反向传播孤波解的全局时间存在性和稳定性。这些解决方案是接近的线性叠加的两个孤波为大的积极和消极的时间值，为中间值的时间，这些解决方案描述了两个反向传播脉冲的相互作用。这些解对于$\ell^2$中的扰动是稳定的，并且对于在空间$\pm \infty$上指数衰减的扰动是渐近稳定的。}
英文摘要：
We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating solitary wave solutions. These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intemediate values of time these solutions describe the interaction of two counterpropagating pulses. These solutions are stable with respect to perturbations in $\ell^2$ and asymptotically stable with respect to perturbations which decay exponentially at spatial $\pm \infty$.}
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