变系数Burgers方程的分类及相似解(英文)

应用经典李群理论考虑了描述非平面冲击波形成和衰减现象的(1 1)维变系数Burgers方程,得到该方程的群分类及相应的对称.对于某些具体形式的色散项系数a(t)和非线性项系数b(t),给出了对应方程的对称约化及相似解.本文在已有基础上给出了方程新的显式解.这些解对于研究某些复杂的物理现象,以及验证数值求解法则的可行性有重要的意义.

Classification and similarity solutions of variable coefficients Burgers equation

The(1 1)-dimensional variable coefficients Burgers equation is considered by using the classical Lie Group theory.Then the classification and corresponding symmetries of the Burgers equation are obtained.Some symmetry reductions are presented for certain forms of a(t) and b(t). To our best knowledge some examples of similarity solutions are given,which maybe provide useful help for physicists to study more complicated physical phenomena and for mathematicians to check on the accuracy and reliability of numerical algorithm.