Gendelman O V, Manevitch L I
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 2):026609. doi: 10.1103/PhysRevE.78.026609. Epub 2008 Aug 22.
We present exact analytic solutions for discrete breathers in essentially nonlinear oscillatory chains, belonging to both of the most common universality classes (Klein-Gordon and Fermi-Pasta-Ulam). The exact solutions can be obtained due to use of vibroimpact potentials, combining extreme nonlinearity with the possibility of description in terms of a forced linear model under conditions of self-consistency. A crossover between the cases of high and low energies can be studied directly. The solutions obtained may be used as a high-energy limit for models with other realistic potentials, as well as benchmarks for the testing of approximate approaches in the theory of discrete breathers.
我们给出了基本非线性振荡链中离散呼吸子的精确解析解，这些振荡链属于两种最常见的普适类（克莱因 - 戈登和费米 - 帕斯塔 - 乌拉姆）。由于使用了振动冲击势，结合了极端非线性以及在自洽条件下用强迫线性模型进行描述的可能性，从而能够得到精确解。可以直接研究高能和低能情况之间的转变。所得到的解可用作具有其他实际势的模型的高能极限，以及离散呼吸子理论中近似方法测试的基准。
