Symmetries of equations with nonlocal terms. (English) Zbl 1416.35022

Meleshko, Sergey V.

Kac, Victor G. (ed.) et al., Symmetries, differential equations and applications. SDEA-III, Istanbul, Turkey, August 14–17, 2017. Selected papers based on the presentations at the conference. Cham: Springer. Springer Proc. Math. Stat. 266, 105-124 (2018).

Summary: An approach for applying group analysis to equations with nonlocal terms is given in the presentation. Similar to the theory of partial differential equations, for invariant solutions of equations with nonlocal terms the number of the independent variables is reduced. The presentation consists of reviewing results obtained by the author with his colleagues related with applications of the group analysis to equations with nonlocal terms such as: integro-differential equations, delay differential equations and stochastic differential equations. The proposed approach can also be applied for defining a Lie group of equivalence, contact and Lie-Bäcklund transformations for equations with nonlocal terms. The presentation is devoted to review the results where the author took a part.
For the entire collection see [Zbl 1405.34003].

MSC:

35B06	Symmetries, invariants, etc. in context of PDEs
35R09	Integro-partial differential equations
35R10	Partial functional-differential equations
35R60	PDEs with randomness, stochastic partial differential equations

Keywords:

Lie group; invariant solution; delay differential equation; stochastic differential equations