In this paper,the supersymmetric Camassa-Holm equation and Degasperis-Procesi equation are derived from a general superfield equations by choosing different parameters.Their peakon-type solutions are shown in weak sen...In this paper,the supersymmetric Camassa-Holm equation and Degasperis-Procesi equation are derived from a general superfield equations by choosing different parameters.Their peakon-type solutions are shown in weak sense.At the same time,the dynamic behaviors are analyzed particularly when the two peakons collide elastically,and some results are compared with each other between the two equations.展开更多
The authors study the multi-soliton, multi-cuspon solutions to the Camassa- Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of para...The authors study the multi-soliton, multi-cuspon solutions to the Camassa- Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of parameters for multi-soliton and multicuspon solutions, especially for n ≥ 3 case. The numerical method （the so-called local discontinuous Galerkin （LDG） method） is also used to simulate the solutions and give the comparison of exact solutions and numerical solutions. The numerical results for the two-soliton and one-cuspon, one-soliton and two-cuspon, three-soliton, three-cuspon, three-soliton and one-cuspon, two-soliton and two-cuspon, one-soliton and three-cuspon, four-soliton and four-cuspon are investigated respectively. by the numerical method for the first time展开更多
We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particu...We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particular, the double peakon solutions of both equations are investigated in detail. At the same time, the dynamic behaviors of three types double peakon solutions are analyzed by some figures.展开更多
基金Supported by the National Science Foundation of China under Grant No. 11071092the Texas Norman Hackerman Advanced Research Program under Grant No. 003599-0001-2009
文摘In this paper,the supersymmetric Camassa-Holm equation and Degasperis-Procesi equation are derived from a general superfield equations by choosing different parameters.Their peakon-type solutions are shown in weak sense.At the same time,the dynamic behaviors are analyzed particularly when the two peakons collide elastically,and some results are compared with each other between the two equations.
基金Project supported by the National Natural Science Foundation of China (Nos.10971211,11031007)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No.200916)+1 种基金the Foundation for the Author of National Excellent Doctoral Dissertation of the Chinese Academy of Sciences,Program for New Century Excellent Talents in University of China (No.09-0922)the Fundamental Research Funds for the Central Universities (No.WK0010000005)
文摘The authors study the multi-soliton, multi-cuspon solutions to the Camassa- Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of parameters for multi-soliton and multicuspon solutions, especially for n ≥ 3 case. The numerical method （the so-called local discontinuous Galerkin （LDG） method） is also used to simulate the solutions and give the comparison of exact solutions and numerical solutions. The numerical results for the two-soliton and one-cuspon, one-soliton and two-cuspon, three-soliton, three-cuspon, three-soliton and one-cuspon, two-soliton and two-cuspon, one-soliton and three-cuspon, four-soliton and four-cuspon are investigated respectively. by the numerical method for the first time
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particular, the double peakon solutions of both equations are investigated in detail. At the same time, the dynamic behaviors of three types double peakon solutions are analyzed by some figures.
