solitary-solution formulation for differential-difference equations using an ancient chinese algorithmsolitary-solution配方为差分方程使用一个中国古代的算法.pdfVIP

Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2012, Article ID 861438, 6 pages doi:10.1155/2012/861438 Research Article Solitary-Solution Formulation for Differential-Difference Equations Using an Ancient Chinese Algorithm Ji-Huan He,1 S. K. Elagan,2, 3 and Guo-Cheng Wu4, 5 1 National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, China 2 Mathematics Statistics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi Arabia 3 Department of Mathematics, Faculty of Science, Menofiya University, Shebin Elkom, Egypt 4 Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, Sichuan 641112, China 5 College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, China Correspondence should be addressed to Ji-Huan He, hejihuan@ Received 6 December 2011; Accepted 10 January 2012 Academic Editor: Allan C. Peterson Copyright q 2012 Ji-Huan He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper applies an ancient Chinese algorithm to differential-difference equations, and a solitary- solution formulation is obtained. The discrete mKdV lattice equation is used as an example to elucidate the solution procedure. 1. Introduction Discrete nonlinear lattices have been the focus of considerable attention in various branches of science. Many differential equations on the nanoscales are invalid, but the problems arising can be well modeled by differential-difference equations 1–5. As is well known, there are many physically interesting problems such as