Lie对称性与KdV孤立波计算中的非线性不稳定性问题(张华彦; 冉政)

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2y!W&iO;k5dx[ s1[0【作者】张华彦; 冉政 【作者单位】上海大学上海市应用数学和力学研究水利论文T r(_%pSn O

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)@c F)q;A-_$}8M.R0【论文摘要】 Kruskal 和 Zabusky 提出的计算孤立子的方法在孤立子理论的发展过程中起了重要作用,但是大量的数值结果表明,即使在满足线性稳定性的参数条件下,该方法也会出现非线性不稳定性的数值现象。本研究通过孤立子数值计算中的异常,由 Kruskal 和 Zabusky 所构造的二阶 Leap-frog 格式得出方程的线性稳定性条件,通过有限差分方法得到该格式的修正方程。运用 Lie 对称群的不变性的分析方法,求出满足 KdV 方程不变的对称群,并讨论了其修正方程以及守恒律是否保持了相应的对称性.研究指出,KdV 方程的守恒律满足了标量变换, 但其数值模拟的修正方程并不满足伽利略变换和标量变换等,也就是说,数值模拟破坏了 KdV 方程的某些物理性质。孤立波计算中的非线性不稳定性与对称性的破缺相关。水利论文F3i pC'x


【英文论文摘要】 The method of calculating the solitons which put forward by Kruskal and Zabusky has played an important role in the development of the soliton theory,however,numerous numerical results show that even though the parameters satisfy the linear stability,nonlinear instability will also appear.In this paper,we noticed the exception in the numerical calcultion of soliton,gained the linear stablity condition of the second order Leap-frog scheme constructed by Kruskal and Zabusky, and then drew the perturbed equation through the finite difference method.After that,we solved the symmetry group of the KdV equation with the knowledge of the invariance of Lie symmetry group and then discussed whether the perturbed equation and the conservation law keep the corresponding symmetry.From the paper,the conservation law of KdV equation satisfies the scaling translation, but the perturbed equation doesn't satisfy the Galilean invariance condition and the scaling invariance condition.That is to say,the nu...更多merical simulation destroyed some physical characteristics of KdV equation.The nonlinear instability in the calculation of solitons relates to the deformity of symmetry.  还原


2[{ V!{0H0【论文关键词】 KdV 孤立波; 非线性不稳定性; Lie 对称性
{,x c-u0l5| b~0【英文论文关键词】 KdV solitons; nonlinear instability; Lie symmetry水利论文w)_ZX6^H p8ik

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TAG: 不稳定性 对称性 冉政 张华彦 KdV
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