On the Application of Conservation Law Multipliers to Find the Linearizing Transformations of Nonlinear PDEs

• Main Authors: Jia-Hong Xie, 謝佳宏
• Other Authors: Po-Jen Cheng
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/20853319598690782074

碩士 === 國立嘉義大學 === 應用數學系研究所 === 99 === In this thesis, we employ Bluman’s direct method to construct conservation laws of the Harry Dym equation and the modifed Harry Dym equation. Linearizing transformations(invertible point or contact transformations) for the Hunter-Saxton equation and the Monge Ap`ere equation are found, respectively, by using the conservation law multiplier method also introduced by Bluman. All calculations are implemented in Maple. Particularly, we use the GeM package to carry out Bluman’s method. It is a Maple package that contains four methods for finding the fluxes of the conservation laws. A Maple program is designed to realize the fifth method which is an algorithm based on flux equations and line integral formulas.