广义KdV-mKdV方程的多辛算法及孤波解数值模拟  

Multi-Symplectic Scheme and Simulation of Solitary Wave Solution for Generalized KdV-mKdV Equation

作　　者：胡伟鹏[1] 邓子辰[1] 李文成[2] 

机构地区：[1]西北工业大学力学与土木建筑学院,陕西西安710072 [2]西北工业大学理学院,陕西西安710072

出　　处：《西北工业大学学报》2008年第4期450-453,共4页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(10572119、10772147和10632030);高校博士点基金(20070699028);陕西省自然科学基金(2006A07);西北工业大学基础研究及大连理工大学工业装备结构分析国家重点实验室开放基金资助

摘　　要：基于Hamilton空间体系的多辛理论研究了广义KdV-mKdV方程。导出了广义KdV-mKdV方程Bridges意义下的多辛形式及其多种守恒律,并构造了相应的Preissmann多辛离散格式及其等价形式。孤波解数值模拟的结果表明:文中构造的多辛格式是有效的,该格式能较好地保持系统的局部能量和动量特性,并具有良好的长时间数值行为及稳定性。Aim. Many practical problems are nonlinear. Linearization often brings poor long-time numerical behavior. In order to keep long-time numerical behavior satisfactory, we consider the multisymplectic formulations of the generalized KdV-mKdV equation with initial value condition in the Hamilton space. In the full paper, we explain our multi-symplectic scheme in some details in this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is. the multisymplectic formulation of the generalized KdV-mKdV equation and its conservation laws. In this topic, we derive eq. （6） as the multi-symplectic formulation and eqs. （7）, （8） and （9） as the conservation laws. The second topic is： the multi-symplectic Preissmann scheme and its equivalent form. In this topic, we construct the equivalent scheme of the Preissmann integrator, which is given as eq. （14）. To verify the validity of eq. （14）, we simulate the solitary wave solution of the generalized KdV-mKdV equation. The computer simulation results, shown in Figs. 1 and 2 in the full paper, indicate preliminarily that the multisymplectic scheme can keep unchanged the wave form of the solitary wave solution and preserve well the local energy and local momentum in the Hamilton space.

关 键 词：数值模拟 广义KdV—mKdV方程 多辛积分 PREISSMANN格式 孤波解 

分 类 号：O241.82[理学—计算数学]