一类广义Camassa-Holm型方程的尖峰孤立波和尖峰孤立波解
PDF下载 (381)刘松林,沃维丰*.一类广义Camassa-Holm型方程的尖峰孤立波和尖峰孤立波解[J].宁波大学学报(理工版),2014,27(03):69-73.DOI:
LIU Song-lin,WO Wei-feng*.Peaked and Periodic Peaked Traveling Wave Solutions for a Generalized Camassa-Holm Type Equation[J].Journal of Ningbo University(Natural Science & Engineering Edition),2014,27(03):69-73.DOI:
| Title: | Peaked and Periodic Peaked Traveling Wave Solutions for a Generalized Camassa-Holm Type Equation |
| 作者: | 刘松林, 沃维丰* |
| Author(s): | LIU Song-lin, WO Wei-feng* |
| 关键词: | Camassa-Holm方程; 修正的Camassa-Holm方程; Degasperis-Procesi方程; 尖峰孤立波解 |
| Keywords: | Camassa-Holm equation; modified Camassa-Holm equation; Degasperis-Procesi equation; peaked traveling wave solution |
| 分类号: | O29 |
| 文献标识码: | A |
| 摘要: | 提出了包含Camassa-Holm方程、修正的Camassa-Holm方程和Degasperis-Procesi方程的一类非线性色散波方程, 并利用一类算子的格林函数结合方程的弱形式解, 得到了这类方程的单个尖峰孤立波解. |
| Abstract: | In this paper, the nonlinear dispersive equations with type-I, including the Camassa-Holm equation, the modified Camassa-Holm equation and the Degasperis-Procesi equation, are proposed. By using the Green function with type-I operator and combining the weak solution of the equation, the peaked traveling wave solution is obtained for the given nonlinear dispersive equations. |
| 参考文献 /References: | [1].Camassa R, Holm D D. An integral shallow water equation with peaked solitons[J]. Phys Rev Lett, 1993, 71:1661-1664. [2].Chou Kaiseng, Qu Changzheng. Integrable equations arising from motions of plane curves[J]. Physica D, 2002, 162:9-33. [3].Constantin A, Lannes D. The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations [J]. Arch Ration Mech Anal, 2009, 192:165-186. [4].Constantin A, Molinet L. Orbital stability of solitary waves for a shallow water equation[J]. Physica D, 2001, 157:75-89. [5].Olver P J, Rosenau P. Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support[J]. Phys Rev E, 1996, 53:1900-1906. [6].Fokas A S. The Korteweg-de Vries equation and beyond[J]. Acta Appl Math, 1995, 39:295-305. [7].Gui Guilong, Liu Yue, Olver P J, et al. Wave-breaking and peakons for a modified Camassa-Holm equation[J]. Comm Math Phy, 2013, 319:731-759. [8].Qu Changzheng, Liu Xiaochuan, Liu Yue. Stability of peakons for an integrable modified Camassa-Holm equation[J]. Comm Math Phys, 2013, 322:967-997. [9].Degasperis A, Procesi M. Asymptotic integrability[J]. Symmetry and Perturbation Theory, 1999, 7:23-37. [10].Constantin A, Lannes D. The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations [J]. Arch Ration Mech Anal, 2009, 192:165-186. [11].Escher J, Liu Yue, Yin Zhaoyang. Global weak solutions and blow-up structure for the Degasperis-Procesi equation[J]. Journal Funct Anal, 2006, 241:457-485. [12].Lin Zhiwu, Liu Yue. Stability of peakons for the Degasperis-Procesi equation[J]. Comm Pure Appl Math, 2009, 62:125-146. |
| 备注/Memo: | 收稿日期: 2013?12?10. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11201249）. 第一作者: 刘松林（1986－）, 男, 河南商丘人, 在读硕士研究生, 主要研究方向: 偏微分方程及其应用. E-mail: liusonglin1015@126.com *通信作者: 沃维丰（1981－）, 女, 浙江宁波人, 博士/讲师, 主要研究方向: 偏微分方程及其应用. E-mail: woweifeng@nbu,edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
