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Multisymplectic box schemes for the complex modified Korteweg–de Vries equation

BROWSE_DETAIL_CREATION_DATE: 29-07-2015

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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: SCIENCE,

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

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BROWSE_DETAIL_DOI: http://dx.doi.org/10.1063/1.3456068

BROWSE_DETAIL_URL: http://www.atilim.edu.tr/~ayhan_ay/pub/JMathPhys_CMKDV.pdf

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In this paper, two multisymplectic integrators, an eight-point Preissman box scheme and a narrow box scheme, are considered for numerical integration of the complex modified Korteweg–de Vries equation. Energy and momentum preservation of both schemes and their dispersive properties are investigated. The performance of both methods is demonstrated through numerical tests on several solitary wavesolutions.


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I. INTRODUCTION

II. MS FORMULATION OF THE CMKdV EQUATION AND THE MS BOX SCHEMESA. MS formulation of the CMKdV equationB. MS box schemes

III. LINEARIZED EQUATIONS AND DISPERSION RELATIONSA. Dispersion relation for the eight-point MS Preissman box schemeB. Dispersion relation for the narrow box scheme

IV. NUMERICAL RESULTSA. Single traveling waveB. The interaction of two traveling wavesV. CONCLUSIONS


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