A multi-symplectic numerical integrator for the two-component Camassa Holm equation

• A new multi-symplectic formulation of the two-component Camassa-Holm equation (2CH) is presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. Furthermore, this scheme preserves exactly two discrete versions of the Casimir functions of 2CH. Numerical experiments show that the proposed numerical scheme has good conservation properties.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

Two-component Camassa-Holm equation

Hamiltonian PDE

Casimir function

Numerical discretisation

Multi-symplectic formulation

Multi-symplectic schemes

Euler box scheme

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