Group classification of linear evolution equations

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• 作者：Alexander Bihlo^a ; ^{abihlo@mun.ca} ; Roman O. Popovych^b ; ^c ; ^{rop@imath.kiev.ua}
• 关键词：Group classification of differential equations ; Lie symmetries ; Equivalence transformations ; Lie reduction ; Linear evolution equations ; Exact solutions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：982-1005
• 全文大小：633 K
• 卷排序：448

文摘

The group classification problem for the class of (1+1)-dimensional linear r  th order evolution equations is solved for arbitrary values of r>2r>2. It is shown that a related maximally gauged class of homogeneous linear evolution equations is uniformly semi-normalized with respect to linear superposition of solutions and hence the complete group classification can be obtained using the algebraic method. We also compute exact solutions for equations from the class under consideration using Lie reduction and its specific generalizations for linear equations.