Open AccessOn the Lie symmetries of the boundary value problems for differential and difference sine-Gordon equations
Author(s) -
Özgür Yıldırım,
Sümeyra Çağlak
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m2/142-153
Subject(s) - mathematics , boundary value problem , mathematical analysis , homogeneous space , differential equation , lie group , free boundary problem , invariant (physics) , ordinary differential equation , mathematical physics , pure mathematics , geometry
In general, due to the nature of the Lie group theory, symmetry analysis is applied to single equations rather than boundary value problems. In this paper boundary value problems for the sine-Gordon equations under the group of Lie point symmetries are obtained in both differential and difference forms. The invariance conditions for the boundary value problems and their solutions are obtained. The invariant discretization of the difference problem corresponding to the boundary value problem for sine-Gordon equation is studied. In the differential case an unbounded domain is considered and in the difference case a lattice with points lying in the plane and stretching in all directions with no boundaries is considered.