Infinite-dimensional symmetries of a general class of variable coefficient evolution equations in 2+1 dimensions

21st International Conference on Integrable Systems and Quantum Symmetries

Basarab-Horwath, P.^1 ; Güngör, F.^2 ; Ozemir, C.^3

Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden^1

Department of Mathematics, Faculty of Science and Sciences, Istanbul Technical University, 34469 Istanbul, Turkey^2

Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, 34469 Istanbul, Turkey^3

关键词: Burgers equations;    Evolution equations;    Exact solution;    General class;    Infinite dimensional;    Lie symmetries;    Painleve;    Variable coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012010/pdf
DOI  :  10.1088/1742-6596/474/1/012010

来源: IOP

【 摘 要 】

We consider generalized KP-Burgers equations and attempt to identify subclasses admitting Virasoro or Kac-Moody type algebras as their symmetries. We give reductions to ODEs constructed from invariance requirement under these infinite-dimensional Lie symmetry algebras and integrate them in cases where it is possible. We also look at the conditions under which the equation passes the Painleve´ test and construct some exact solutions by truncation.