›› 2014, Vol. 23 ›› Issue (11): 110203-110203.doi: 10.1088/1674-1056/23/11/110203
刘希忠a, 俞军a, 任博a, 杨建荣b
Liu Xi-Zhong (刘希忠)a, Yu Jun (俞军)a, Ren Bo (任博)a, Yang Jian-Rong (杨建荣)b
摘要: We obtain the non-local residual symmetry related to truncated Painlevé expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also localize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th Bäcklund transformation for Burgers equation can be expressed by determinants in a compact way.
中图分类号: (Partial differential equations)