A formula for symmetry recursion operators from non-variational symmetries of partial differential equations

被引：0
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作者：
Stephen C. Anco
Bao Wang
机构：
[1] Brock University,Department of Mathematics and Statistics
[2] Ningbo University,School of Mathematics and Statistics
来源：
Letters in Mathematical Physics | 2021年 / 111卷
关键词：
Symmetry; Non-variational; Adjoint-symmetry; Multiplier; Non-multiplier; Recursion operator; Hamiltonian operator; Symplectic operator; 58J70; 35A30; 35A15; 70H06;
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摘要：
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a general formula that produces a pre-symplectic operator from a non-gradient adjoint-symmetry. These formulas are illustrated by several examples of linear PDEs and integrable nonlinear PDEs. Additionally, a classification of quasilinear second-order PDEs admitting a multiplicative symmetry recursion operator through the first formula is presented.
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