论文信息 - Multisymplecticity and wave action conservation

Multisymplecticity and wave action conservation

This paper discuses some novel results concerning the wave action conservation law for multisymplectic partial differential equations and their discretizations. We provide a method for deriving this conservation law in Fourier spectral space. A discrete wave action conservation law for a multisymplectic box scheme and for the midpoint time-discretization of a spectral method is also derived.

Constance M. Schober | Tomasz H. Wlodarczyk | C. Schober | T. Wlodarczyk

[1] S. Reich,et al. Multi-symplectic spectral discretizations for the Zakharov–Kuznetsov and shallow water equations , 2001 .

[2] V. Arnold. Mathematical Methods of Classical Mechanics , 1974 .

[3] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[4] T. Bridges. A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5] Brian E. Moore,et al. Backward error analysis for multi-symplectic integration methods , 2003, Numerische Mathematik.

[6] C. Schober,et al. On the preservation of phase space structure under multisymplectic discretization , 2004 .

[7] G. Whitham,et al. Linear and Nonlinear Waves , 1976 .

[8] E. Hairer,et al. Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[9] J. M. Sanz-Serna,et al. Numerical Hamiltonian Problems , 1994 .

[10] J. Frank. Conservation of wave action under multisymplectic discretizations , 2006 .