English

Continuous changes of variables and the Magnus expansion

Mathematical Physics 2019-10-29 v1 Classical Analysis and ODEs math.MP Classical Physics

Abstract

In this paper, we are concerned with a formulation of Magnus and Floquet-Magnus expansions for general nonlinear differential equations. To this aim, we introduce suitable continuous variable transformations generated by operators. As an application of the simple formulas so-obtained, we explicitly compute the first terms of the Floquet-Magnus expansion for the Van der Pol oscillator and the nonlinear Schr\"odinger equation on the torus.

Keywords

Cite

@article{arxiv.1907.05362,
  title  = {Continuous changes of variables and the Magnus expansion},
  author = {Fernando Casas and Philippe Chartier and Ander Murua},
  journal= {arXiv preprint arXiv:1907.05362},
  year   = {2019}
}

Comments

19 pages, 2 figures