Heteroclinic orbits for a higher order phase transition problem
Heteroclinic orbits for a higher order phase transition problem
复制标题
高阶相变问题的异斜轨道
DOI：
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发表时间：
1997
影响因子：
1.9
通讯作者：
Xiaofeng Ren
中科院分区：
文献类型：
--
作者：
P. Bates;Xiaofeng Ren
一维相变的标准模型是具有非线性项的二阶半线性方程，其中寻求连接两个稳定值的解。从一个类伊辛模型，但其中包括长程相互作用，导致考虑方程的二阶算子被替换为任意高阶之一。其他人已经找到了这样的方程所需的异宿解，假设高阶项具有小的系数，通过采用奇异摄动方法的动力系统。在这里，不作任何假设的系数的大小，我们得到这样的异宿解，通过使用变分方法的假设下，非线性产生的潜在的两个威尔斯的深度相等。
A standard model for one-dimensional phase transitions is the second-order semilinear equation with bistable nonlinearity, where one seeks a solution which connects the two stable values. From an Ising-like model but which includes long-range interaction, one is led to consider the equation where the second-order operator is replaced by one of arbitrarily high order. Others have found the desired heteroclinic solutions for such equations, under the assumption that the higher-order terms have small coefficients, by employing singular perturbation methods for dynamical systems. Here, without making any assumption on the sizes of the coefficients, we obtain such heteroclinic solutions by using variational methods under the assumption that the nonlinearity arises from a potential having two wells of equal depths.