Energy preserving integration of bi-Hamiltonian partial differential equations

Karas?zen B.; ?im?ek G.

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Energy preserving integration of bi-Hamiltonian partial differential equations

机译：双哈密顿偏微分方程的能量守恒积分

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The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating waves and solitons. Dispersive properties of the AVF integrator are investigated for the linearized equations to examine the nonlinear dynamics after discretization.

机译：能量守恒的平均矢量场（AVF）积分器应用于具有非恒定Poisson结构的双哈密尔顿形式的演化偏微分方程（PDE）。 Korteweg de Vries（KdV）方程和Ito型耦合KdV方程的数值结果证实了Hamiltonian和Casimir积分的长期保存，这对于模拟波和孤子至关重要。对AVF积分器的色散特性进行了线性化方程研究，以检验离散后的非线性动力学。

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《Applied mathematics letters》 |2013年第12期|共9页
作者
Karas?zen B.; ?im?ek G.;
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正文语种 eng
中图分类应用数学;
关键词
Bi-Hamiltonian systems; Dispersion; Energy preservation; Korteweg de Vries equation; Poisson structure;

机译：双哈密顿体系;色散;能量守恒;Korteweg de Vries方程;泊松结构;

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Energy preserving integration of bi-Hamiltonian partial differential equations

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