Group Analysis Of Differential Equations

Group analysis of differential equations is a branch of mathematics that studies the symmetry properties of differential equations with respect to various transformations of independent and dependent variables. It includes methods and applied aspects of differential geometry, Lie groups and algebras theory, calculus of variations and is, in turn, a powerful research tool in theories of ODEs, PDEs, mathematical and theoretical physics.^[1]^[2]^[3]

Motivation

References

↑ Ovsyannikov, Lev V. (1982). Group analysis of differential equations. Academic Press. ISBN 9781483219066. https://books.google.com/books?id=YpPiBQAAQBAJ&pg=PA1.
↑ Olver, Peter J. (1986). Applications of Lie groups to differential equations. Graduate Texts in Mathematics. 107. Springer-Verlag New York. doi:10.1007/978-1-4684-0274-2. ISBN 978-1-4684-0274-2. https://www.springer.com/gp/book/9781468402742.
↑ Ibragimov, Nail H. (1985). Transformation groups applied to mathematical physics. Mathematics and its Applications. 3. Springer Netherlands. ISBN 978-90-277-1847-1. https://www.springer.com/gp/book/9789027718471.

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[1] Ovsyannikov, Lev V. (1982). Group analysis of differential equations. Academic Press. ISBN 9781483219066. https://books.google.com/books?id=YpPiBQAAQBAJ&pg=PA1.

[2] Olver, Peter J. (1986). Applications of Lie groups to differential equations. Graduate Texts in Mathematics. 107. Springer-Verlag New York. doi:10.1007/978-1-4684-0274-2. ISBN 978-1-4684-0274-2. https://www.springer.com/gp/book/9781468402742.

[3] Ibragimov, Nail H. (1985). Transformation groups applied to mathematical physics. Mathematics and its Applications. 3. Springer Netherlands. ISBN 978-90-277-1847-1. https://www.springer.com/gp/book/9789027718471.