Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

483 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

MULTI-SYMPLECTIC FOURIER PSEUDOSPECTRAL METHOD FOR THE NONLINEAR SCHR ¨ ODINGER EQUATION (2001, unknown): “We consider the nonlinear Schrödinger equation iψt + ψxx + a|ψ|2ψ = 0(1.1) with the periodic boundary condition ψ(0, t) = ψ(L, t).”
Solving the nonlinear Schrodinger equation using exponential integrators (2006, background): “For long-time integration where stability and preservation of invariants is an important factor, multisymplectic schemes may be a viable choice [3, 10].”
Numerical Methods for Evolutionary Differential Equations (2008, background): “– It has a multisymplectic structure; see [36, 37, 188, 11] and Exercise 9.”
Numerical methods for Hamiltonian PDEs (2006, methodology): “General aspects of the theory of modified conservation laws is developed in Moore & Reich [109].”
Multisymplectic box schemes and the Korteweg{de Vries equation (2004, background): “It has recently been proposed that hyperbolic systems which are “multisymplectic” (symplectic in both space and time) should be discretized so as to preserve this structure [5,13].”