Higher-order accurate Runge-Kutta discontinuous Galerkin methods fora nonlinear Dirac model
Higher-order accurate Runge-Kutta discontinuous Galerkin methods fora nonlinear Dirac model
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DOI：
10.3934/dcdsb.2006.6.623
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发表时间：
2006-02
影响因子：
1.2
通讯作者：
Sihong Shao;Huazhong Tang
中科院分区：
文献类型：
--
作者：
Sihong Shao;Huazhong Tang
本文将龙格-库塔不连续伽辽金（RKDG）方法扩展到相对论量子物理中的非线性狄拉克（NLD）模型，并研究相应的孤立波解的相互作用动力学。通过在更精细的网格上使用高阶精确方案，首先观察到三元碰撞中的弱非弹性相互作用。两个驻波碰撞时，以近似恒定的频率形成长寿命的振荡状态；另一个是两个移动孤子碰撞的频率不断增加。我们还证明了 NLD 模型的三个连续统守恒定律和半离散 RKDG 方法的熵不等式（即总电荷不增），并通过各种数值例子进行了证明。
This paper extends Runge-Kutta discontinuous Galerkin (RKDG) methods to a nonlinear Dirac (NLD) model in relativistic quantum physics, and investigates interaction dynamics of corresponding solitary wave solutions. Weak inelastic interaction in ternary collisions is first observed by using high-order accurate schemes on finer meshes. A long-lived oscillating state is formed with an approximate constant frequency in collisions of two standing waves; another is with an increasing frequency in collisions of two moving solitons. We also prove three continuum conservation laws of the NLD model and an entropy inequality, i.e. the total charge non-increasing, of the semi-discrete RKDG methods, which are demonstrated by various numerical examples.