A direct algorithm of one-dimensional optimal system for the group invariant solutions
Xiaorui HuZhejiang University of Technology 1 Department of Applied Mathematics, , Hangzhou 310023, People’s Republic of ChinaYuqi LiEast China Normal University 2 Shanghai Key Laboratory of Trustworthy Computing, , Shanghai 200062, People’s Republic of ChinaYong ChenEast China Normal University 2 Shanghai Key Laboratory of Trustworthy Computing, , Shanghai 200062, People’s Republic of China
2015en
ABI
Annotatsiya
A direct and systematic algorithm is proposed to find one-dimensional optimal system for the group invariant solutions, which is attributed to the classification of its corresponding one-dimensional Lie algebra. Since the method is based on different values of all the invariants, the process itself can both guarantee the comprehensiveness and demonstrate the inequivalence of the optimal system, with no further proof. To leave the algorithm clear, we illustrate each stage with a couple of well-known examples: the Korteweg-de Vries equation and the heat equation. Finally, we apply our method to the Novikov equation and use the found optimal system to investigate the corresponding invariant solutions.
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