Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.09040 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910297510379520 |
|---|---|
| author | White, Lewis C. Hydon, Peter E. |
| author_facet | White, Lewis C. Hydon, Peter E. |
| contents | This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising from Noether's theorem. The differential-difference theory is not merely an amalgam of the differential and difference theories, but has additional features that reflect the need for the group action to preserve the prolongation structure. Projectable moving frames are introduced; these cause the invariant derivative operator to commute with shifts in the discrete variables. Examples include a Toda-type equation and a method of lines semi-discretization of the nonlinear Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09040 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moving Frames: Difference and Differential-Difference Lagrangians White, Lewis C. Hydon, Peter E. Mathematical Physics 39A14, 58D19, 47E07 This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising from Noether's theorem. The differential-difference theory is not merely an amalgam of the differential and difference theories, but has additional features that reflect the need for the group action to preserve the prolongation structure. Projectable moving frames are introduced; these cause the invariant derivative operator to commute with shifts in the discrete variables. Examples include a Toda-type equation and a method of lines semi-discretization of the nonlinear Schrödinger equation. |
| title | Moving Frames: Difference and Differential-Difference Lagrangians |
| topic | Mathematical Physics 39A14, 58D19, 47E07 |
| url | https://arxiv.org/abs/2309.09040 |