非线性热传导方程的几类精确解  

Several Types of Exact Solutions of the Nonlinear Heat Conduction Equation

作　　者：郭鹏[1,2] 陈宗广[1] 孙小伟[1] 彭一春 GUO Peng;CHEN Zong-guang;SUN Xiao-wei;PENG Yi-chun(School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China;Key Laboratory of Railway Vehicle Thermal Engineering, Ministry of Education, Lanzhou Jiaotong University, Lanzhou 730070, China;School of Civil Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]兰州交通大学铁道车辆热工教育部重点实验室,甘肃兰州730070 [3]兰州工业学院土木工程学院,甘肃兰州730050

出　　处：《数学的实践与认识》2018年第2期179-183,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11464027);甘肃省自然科学基金(1506RJZA074,1310RJZA076);兰州交通大学青年科学基金(2014023,2016012)

摘　　要：通过引入恰当的试探函数，将非线性热传导方程化为易于求解的常微分方程组并对其求解，进而得到非线性热传导方程的孤波解、奇异行波解、三角函数周期波解等一些不同形式的行波解．Introducing suitable trial function, the nonlinear heat conduction equation duced into a simple solvable system of ordinary differential equations. Some solitary solutions, singular travelling wave solutions, and trigonometric function periodic wave tions are obtained by solving the system of ordinary differential equations. IS rewave

关 键 词：试探函数方法 非线性热传导方程 精确解 孤子 

分 类 号：O175[理学—数学]