Energy preserving integration of KdV-KdV systems

Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results confirm long term preservation of the energy and the quadratic invariants. Produced generalized solitary waves are similar to those in the litera...

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Published inTWMS journal of applied and engineering mathematics Vol. 2; no. 2; pp. 219 - 227
Main Authors Karasozen, Bulent, Simsek, Gorkem
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.07.2012
Elman Hasanoglu
Subjects
Differential equations, Partial
Fields (mathematics)
Hamiltonian functions
Hamiltonian systems
Invariants
Mathematical analysis
Mathematical models
Mathematical research
Mathematics
Preserving
Solitary waves
Traveling waves
Vector space
Vector spaces
Turkey
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ISSN2146-1147
2146-1147

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Abstract Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results confirm long term preservation of the energy and the quadratic invariants. Produced generalized solitary waves are similar to those in the literature for larger mesh sizes and time steps. Numerical and continuous dispersion relations of the linearized equations are compared to analyze the behavior of the traveling waves and the interaction of the solitons.
AbstractList Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results confirm long term preservation of the energy and the quadratic invariants. Produced generalized solitary waves are similar to those in the literature for larger mesh sizes and time steps. Numerical and continuous dispersion relations of the linearized equations are compared to analyze the behavior of the traveling waves and the interaction of the solitons.
Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results confirm long term preservation of the energy and the quadratic invariants. Produced generalized solitary waves are similar to those in the literature for larger mesh sizes and time steps. Numerical and continuous dispersion relations of the linearized equations are compared to analyze the behavior of the traveling waves and the interaction of the solitons. Keywords: Energy preservation, bi-Hamiltonian systems, Poisson structure, KdV equation, dispersion. AMS Subject Classification: 65P10, 65L06, 37K10.
Audience Academic
Author Simsek, Gorkem
Karasozen, Bulent
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Copyright COPYRIGHT 2012 Turkic World Mathematical Society
Copyright Elman Hasanoglu 2012
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Elman Hasanoglu
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Snippet Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results...
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SubjectTerms Differential equations, Partial
Fields (mathematics)
Hamiltonian functions
Hamiltonian systems
Invariants
Mathematical analysis
Mathematical models
Mathematical research
Mathematics
Preserving
Solitary waves
Traveling waves
Vector space
Vector spaces
Title Energy preserving integration of KdV-KdV systems
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