格点动力系统多脉冲解的孤立点
Isolas of multi-pulse solutions to lattice dynamical systems
摘要：
研究了一类非线性格点动力系统多脉冲稳态解的存在性和分支结构。这样的解决方案的特点是由多个紧凑的不连通区域的解决方案类似于一个的状态，并类似于另一个平凡的状态以外的这些紧凑的集合。结果表明，这些多脉冲解的分叉曲线位于封闭和有界的曲线（隔离），即使当单脉冲解位于无界曲线。这些结果被应用到一个离散的Nagumo微分方程，我们表明，这项工作的假设可以证实分析附近的反连续极限。结果证明了一些数值调查。
英文摘要：
This work investigates the existence and bifurcation structure of multi-pulse steady-state solutions to bistable lattice dynamical systems. Such solutions are characterized by multiple compact disconnected regions where the solution resembles one of the bistable states and resembles another trivial bistable state outside of these compact sets. It is shown that the bifurcation curves of these multi-pulse solutions lie along closed and bounded curves (isolas), even when single-pulse solutions lie along unbounded curves. These results are applied to a discrete Nagumo differential equation and we show that the hypotheses of this work can be confirmed analytically near the anti-continuum limit. Results are demonstrated with a number of numerical investigations.
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