Bihlo, Alexander; Coiteux-Roy, Xavier; Winternitz, Pavel The Korteweg-de Vries equation and its symmetry-preserving discretization. (English) Zbl 1319.35214 J. Phys. A, Math. Theor. 48, No. 5, Article ID 055201, 25 p. (2015). Authors’ abstract: The Korteweg-de Vries equation is one of the most important nonlinear evolution equations in the mathematical sciences. In this article invariant discretization schemes are constructed for this equation both in the Lagrangian and in the Eulerian form. We also propose invariant schemes that preserve the momentum. Numerical tests are carried out for all invariant discretization schemes and related to standard numerical schemes. We find that the invariant discretization schemes give generally the same level of accuracy as the standard schemes with the added benefit of preserving Galilean transformations which is demonstrated numerically as well. Reviewer: Anthony D. Osborne (Keele) Cited in 5 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35G25 Initial value problems for nonlinear higher-order PDEs 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:invariant discretization; Korteweg-de Vries equation; moving meshes PDFBibTeX XMLCite \textit{A. Bihlo} et al., J. Phys. A, Math. Theor. 48, No. 5, Article ID 055201, 25 p. (2015; Zbl 1319.35214) Full Text: DOI arXiv