GeometricNumerical Integration for Peakon b-Family Equations  

作　　者：Wenjun Cai Yajuan Sun Yushun Wang 

机构地区：[1]Key Laboratory of Computational Geodynamics,University of Chinese Academy of Sciences,Beijing 100049,China [2]LSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]Jiangsu Provincial Key Laboratory for NSLSCS,School of Mathematical Sciences,Nanjing Normal University Nanjing 210023,China

出　　处：《Communications in Computational Physics》2016年第1期24-52,共29页计算物理通讯（英文）

基　　金：This research was supported by the National Natural Science Foundation of China 11271357,11271195 and 41504078;by the CSC,the Foundation for Innovative Research Groups of the NNSFC 11321061 and the ITER-China Program 2014GB124005。

摘　　要：In this paper,we study the Camassa-Holm equation and the Degasperis-Procesi equation.The two equations are in the family of integrable peakon equations,and both have very rich geometric properties.Based on these geometric structures,we construct the geometric numerical integrators for simulating their soliton solutions.The Camassa-Holm equation and the Degasperis-Procesi equation have many common properties,however they also have the significant difference,for example there exist the shock wave solutions for the Degasperis-Procesi equation.By using the symplectic Fourier pseudo-spectral integrator,we simulate the peakon solutions of the two equations.To illustrate the smooth solitons and shock wave solutions of the DP equation,we use the splitting technique and combine the composition methods.In the numerical experiments,comparisons of these two kinds of methods are presented in terms of accuracy,computational cost and invariants preservation.

关 键 词：Symplectic integrator splitting method WENO scheme multisymplectic integrator PEAKON shockpeakon 

分 类 号：O17[理学—数学]