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Symplectic and Multisymplectic Lobatto Methods For The “good” Boussinesq Equation

BROWSE_DETAIL_CREATION_DATE: 07-09-2015

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BROWSE_DETAIL_TYPE: Article

BROWSE_DETAIL_PUBLISH_STATE: Published

BROWSE_DETAIL_FORMAT: No File

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: Mathematics, SCIENCE,

BROWSE_DETAIL_CREATORS: Aydin , Ayhan (Author), Karasözen, Bülent (Author),

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Symplectic Lobatto methods, multisymplectic Lobatto methods


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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 preserving local and global energy and momentum.


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I. INTRODUCTIONII. SYMPLECTIC INTEGRATIONIII. MULTISYMPLECTIC INTEGRATIONIV. DISCRETIZATION OF THE CONSERVED QUANTITIESV. LINEARIZED EQUATIONS AND DISPERSION RELATIONSVI. LINEAR STABILITY ANALYSISVII. NUMERICAL RESULTSA. Single solitary waveB. Colliding solitary wavesVIII. CONCLUSIONS


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