Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation

Dmytro R. Popovych, Serhii D. Koval, Roman O. Popovych
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Abstract

Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of ultraparabolic linear second-order partial differential equations with three independent variables by its wonderful symmetry properties. It turns out that the essential part of this algebra is generated by the recursion operators associated with the nilradical of the essential Lie invariance algebra of the Kolmogorov equation, and the Casimir operator of the Levi factor of the latter algebra unexpectedly arises in the consideration.
非凡 (1+2) 维福克-普朗克方程的广义对称性
该方程又称科尔莫哥罗夫方程,以其奇妙的对称性在三自变量超平抛线性二阶偏微分方程中脱颖而出。事实证明,该代数的基本部分是由与科尔莫哥洛夫方程的基本李不变性代数的零根相关的递归算子生成的,而后者代数的列维因子的卡西米尔算子则出乎意料地出现在研究中。
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