Multisymplectic structures for one-way wave equations are presented in this letter. Based on the multisymplectic formulation, we obtain the corresponding multisymplectic discretizations. The structure-preserving property of a finite difference scheme for the first-order one-way wave equation is proved. Implications and applications of this result are explored.
Mathematics Subject Classification (2000)
multisymplectic discretization one-way equation
This is a preview of subscription content, log in to check access.
Chen J.B. (2002) Multisymplecticity of Crank-Nicolson scheme for the nonlinear Schrödinger equation. J. Phys. Soc. J. 71, 2348–2349MATHCrossRefGoogle Scholar
Chen J.B. (2002) Total variation in discrete multisymplectic field theory and multisymplectic energy momentum integrators. Lett. Math. Phys. 61, 63–73MATHCrossRefMathSciNetGoogle Scholar
Chen J.B. (2003) Multisymplectic geometry, local conservation laws and a multisymplectic integrator for the Zakharov-Kuznetsov equation. Lett. Math. Phys. 63, 115–124MATHCrossRefMathSciNetGoogle Scholar
Claerbout J.F. (1985) Imaging the Earth’s Interior. Blackwell, OxfordGoogle Scholar
Ma Z.T. (1989) Seismic imaging techniques: finite-difference migration. Oil Industry Press, BeijingGoogle Scholar
Reich S. (2000) Multisymplectic Runge-Kutta collocation methods for Hamiltonian wave equations. J. Comp. Phys. 157, 473–499MATHCrossRefADSGoogle Scholar
Ristow D., Rühl T. (1997) 3-D implicit finite-difference migration by multiway splitting. Geophysics 62, 554–567CrossRefGoogle Scholar