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Article Citation - WoS: 24Citation - Scopus: 24Symplectic and multisymplectic Lobatto methods for the "good" Boussinesq equation(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.In this paper, we construct second order symplectic and multisymplectic integrators for the "good" Boussineq equation using the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method, which yield an explicit scheme and is equivalent to the classical central difference approximation to the second order spatial derivative. Numerical dispersion properties and the stability of both integrators are investigated. Numerical results for different solitary wave solutions confirm the excellent long time behavior of symplectic and multisymplectic integrators by preservink local and global energy and momentum. (C) 2008 American Institute of Physics.Conference Object Citation - WoS: 1Multisymplectic Schemes for the Complex Modified Korteweg-De Vries Equation(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.
