一个可积的逆空时非局部Sasa-Satsuma方程

宋彩芹; 朱佐农

doi:10.7498/aps.69.20191887

摘要

本文给出了一个可积的逆空时(逆空间-逆时间)非局部Sasa-Satsuma方程. 建立了这个方程的Darboux变换, 并且构造了这个逆空时非局部方程在零背景条件下的孤子解.

关键词:

Abstract

In this paper, we introduce an integrable reverse space-time nonlocal Sasa-Satsuma equation. The Darboux transformation and soliton solutions for this nonlocal integrable equation are constructed.

Keywords:

integrable reverse space-time nonlocal Sasa-Satsuma equation /
Darboux transformation /
soliton solution

作者及机构信息

宋彩芹¹,
朱佐农²

1.
上海理工大学理学院, 上海　200093

2.
上海交通大学数学科学学院, 上海　200240

通信作者: 朱佐农, znzhu@sjtu.edu.cn

基金项目: 国家自然科学基金(批准号: 11671255, 11801367)资助的课题

Authors and contacts

Song Cai-Qin¹,
Zhu Zuo-Nong²

1.
College of Sciences, University of Shanghai for Science and Technology, Shanghai 200093, China

2.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding author: Zhu Zuo-Nong, znzhu@sjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.11671255, 11801367)

文章全文 : translate this paragraph

参考文献

[1]	Sasa N, Satsuma J 1991 J. Phys. Soc. Jpn 60 409 Google Scholar
[2]	Porsezian K, Nakkeeran K 1996 Phys. Rev. Lett 76 3955 Google Scholar
[3]	Mihalache D, Torner L, Moldoveanu F, Panoiu N C, Truta N 1993 Phys. Rev. E 48 4699 Google Scholar
[4]	Ghosh S, Kundu A, Nandy S 1999 J. Math. Phys. 40 1993 Google Scholar
[5]	Li Y S, Han W T 2001 Chin. Ann. Math. 22B 171
[6]	Gilson C, Hietarinta J, Nimmo J, Ohta Y 2003 Phys. Rev. E 68 016614 Google Scholar
[7]	Wright O C 2007 Chaos, Solitons Fractals 33 374
[8]	Nimmo J, Yilmaz H 2015 J. Phys. A. Math. Theor. 48 425202 Google Scholar
[9]	Bandelow U, Akhmediev N 2012 Phys. Rev. E 86 026606 Google Scholar
[10]	Li Z H, Li L, Tian H P, Zhou G S 2000 Phys. Rev. Lett. 84 4096 Google Scholar
[11]	Ohta Y 2010 AIP Conference Proceeding 1212 114
[12]	Zhao L C, Li S C, Ling L M 2014 Phys. Rev. E 89 023210 Google Scholar
[13]	Xu T, Li M, Li L 2015 Europhys. Lett. 109 30006 Google Scholar
[14]	Liu Y K, Li B 2017 Chin. Phys. Lett. 34 010202 Google Scholar
[15]	Ablowitz M J, Musslimani Z H 2013 Phys. Rev. Lett. 110 064105 Google Scholar
[16]	Ablowitz M J, Musslimani Z H 2016 Stud. Appl. Math. 139 7
[17]	Ji J L, Zhu Z N 2017 Commun. Nonlinear Sci. Numer. Simul. 42 699 Google Scholar
[18]	Lou S Y 2018 J. Math. Phys. 59 083507 Google Scholar
[19]	Yang B, Yang J 2018 Stud. Appl. Math 140 178 Google Scholar
[20]	Song C Q, Xiao D M, Zhu Z N 2017 J. Phys. Soc. Jpn. 86 054001 Google Scholar
[21]	Rao J, Cheng Y, He J S 2017 Stud. Appl. Math. 139 568 Google Scholar
[22]	Rao J, Cheng Y, Porsezian K, Mihalache S, He J S 2020 Physica D 401 132180 Google Scholar
[23]	Ji J L, Zhu Z N 2017 J. Math. Anal. Appl. 453 973 Google Scholar
[24]	Ma L Y, Zhu Z N 2016 J. Math. Phys. 57 083507 Google Scholar

施引文献

图 1 可积的逆空时非局部Sasa-Satsuma方程(7)的孤子解　(a) α₁ = α₂ = β₁ = β₂ = $ \dfrac{\sqrt{2}}{2}, \lambda_1 = {\rm i}, \lambda_2 = -{\rm i}/2 $; (b) α₁ = –α₂ = β₁ = –β₂ = $ \dfrac{\sqrt{2}}{2}, \lambda_1 = 1+{\rm i}, \lambda_2 = 1-{\rm i} $; (c) α₁ = β₁ = 1, α₂ = β₂ = 0 $\lambda_2 = {\rm i}, \lambda_1 = \dfrac{1-\sqrt{2}}{1+\sqrt{2}}\lambda_2 $

Fig. 1. Soliton solutions of integrable reverse space-time nonlocal Sasa-Satsuma equation (7): (a) α₁ = α₂ = β₁ = β₂ = $ \dfrac{\sqrt{2}}{2}, \lambda_1 = {\rm i}, \lambda_2 = -{\rm i}/2 $; (b) α₁ = –α₂ = β₁ = –β₂ = $ \dfrac{\sqrt{2}}{2}, $ $\lambda_1 = 1+{\rm i}, \lambda_2 = 1-{\rm i} $; (c) α₁ = β₁ = 1, α₂ = β₂ = 0 $\lambda_2 = {\rm i}, \lambda_1 = \dfrac{1-\sqrt{2}}{1+\sqrt{2}}\lambda_2 $

下载: 全尺寸图片幻灯片

[1]	Sasa N, Satsuma J 1991 J. Phys. Soc. Jpn 60 409 Google Scholar
[2]	Porsezian K, Nakkeeran K 1996 Phys. Rev. Lett 76 3955 Google Scholar
[3]	Mihalache D, Torner L, Moldoveanu F, Panoiu N C, Truta N 1993 Phys. Rev. E 48 4699 Google Scholar
[4]	Ghosh S, Kundu A, Nandy S 1999 J. Math. Phys. 40 1993 Google Scholar
[5]	Li Y S, Han W T 2001 Chin. Ann. Math. 22B 171
[6]	Gilson C, Hietarinta J, Nimmo J, Ohta Y 2003 Phys. Rev. E 68 016614 Google Scholar
[7]	Wright O C 2007 Chaos, Solitons Fractals 33 374
[8]	Nimmo J, Yilmaz H 2015 J. Phys. A. Math. Theor. 48 425202 Google Scholar
[9]	Bandelow U, Akhmediev N 2012 Phys. Rev. E 86 026606 Google Scholar
[10]	Li Z H, Li L, Tian H P, Zhou G S 2000 Phys. Rev. Lett. 84 4096 Google Scholar
[11]	Ohta Y 2010 AIP Conference Proceeding 1212 114
[12]	Zhao L C, Li S C, Ling L M 2014 Phys. Rev. E 89 023210 Google Scholar
[13]	Xu T, Li M, Li L 2015 Europhys. Lett. 109 30006 Google Scholar
[14]	Liu Y K, Li B 2017 Chin. Phys. Lett. 34 010202 Google Scholar
[15]	Ablowitz M J, Musslimani Z H 2013 Phys. Rev. Lett. 110 064105 Google Scholar
[16]	Ablowitz M J, Musslimani Z H 2016 Stud. Appl. Math. 139 7
[17]	Ji J L, Zhu Z N 2017 Commun. Nonlinear Sci. Numer. Simul. 42 699 Google Scholar
[18]	Lou S Y 2018 J. Math. Phys. 59 083507 Google Scholar
[19]	Yang B, Yang J 2018 Stud. Appl. Math 140 178 Google Scholar
[20]	Song C Q, Xiao D M, Zhu Z N 2017 J. Phys. Soc. Jpn. 86 054001 Google Scholar
[21]	Rao J, Cheng Y, He J S 2017 Stud. Appl. Math. 139 568 Google Scholar
[22]	Rao J, Cheng Y, Porsezian K, Mihalache S, He J S 2020 Physica D 401 132180 Google Scholar
[23]	Ji J L, Zhu Z N 2017 J. Math. Anal. Appl. 453 973 Google Scholar
[24]	Ma L Y, Zhu Z N 2016 J. Math. Phys. 57 083507 Google Scholar

[1]	姚慧, 张海强, 熊玮玥. 椭圆函数背景下Gerdjikov-Ivanov方程的多呼吸子. 物理学报, 2024, 73(4): 040201. doi: 10.7498/aps.73.20231590
[2]	楼森岳. 可积系统多孤子解的全反演对称表达式. 物理学报, 2020, 69(1): 010503. doi: 10.7498/aps.69.20191172
[3]	钱存, 王亮亮, 张解放. 变系数非线性Schrödinger方程的孤子解及其相互作用. 物理学报, 2011, 60(6): 064214. doi: 10.7498/aps.60.064214
[4]	莫嘉琪, 姚静荪. 扰动KdV方程孤子的同伦映射解. 物理学报, 2008, 57(12): 7419-7422. doi: 10.7498/aps.57.7419
[5]	刘红, 魏佳羽, 楼森岳, 贺贤土. 一维Tonks-Girardeau原子气区域中的亮孤子解. 物理学报, 2008, 57(3): 1343-1346. doi: 10.7498/aps.57.1343
[6]	贺锋, 郭启波, 刘辽. 用三角函数法获得非线性Boussinesq方程的广义孤子解. 物理学报, 2007, 56(8): 4326-4330. doi: 10.7498/aps.56.4326
[7]	蒲利春, 张雪峰, 徐丽君. 非线性“loop”孤子方程的确定解. 物理学报, 2005, 54(9): 4186-4191. doi: 10.7498/aps.54.4186
[8]	韦才敏, 夏尊铨, 田乃硕. 广义随机KdV方程新的精确类孤子解. 物理学报, 2005, 54(6): 2463-2467. doi: 10.7498/aps.54.2463
[9]	张解放, 徐昌智, 何宝钢. 变量分离法与变系数非线性薛定谔方程的求解探索. 物理学报, 2004, 53(11): 3652-3656. doi: 10.7498/aps.53.3652
[10]	付遵涛, 刘式适, 刘式达. 非线性波方程求解的新方法. 物理学报, 2004, 53(2): 343-348. doi: 10.7498/aps.53.343
[11]	赵长海, 盛正卯. Zakharov方程的显式行波解. 物理学报, 2004, 53(6): 1629-1634. doi: 10.7498/aps.53.1629
[12]	唐驾时, 刘铸永, 李学平. MKdV方程的拟小波解. 物理学报, 2003, 52(3): 522-525. doi: 10.7498/aps.52.522
[13]	赵熙强, 唐登斌, 王利民, 张耀明. 高阶(2+1)维Broer-Kaup方程的孤波解. 物理学报, 2003, 52(8): 1827-1831. doi: 10.7498/aps.52.1827
[14]	徐桂琼, 李志斌. 两个非线性发展方程的双向孤波解与孤子解. 物理学报, 2003, 52(8): 1848-1857. doi: 10.7498/aps.52.1848
[15]	周振江, 李志斌. Broer-Kaup系统的达布变换和新的精确解. 物理学报, 2003, 52(2): 262-266. doi: 10.7498/aps.52.262
[16]	李画眉. (3+1)维Nizhnik-Novikov-Veselov方程的孤子解和周期解. 物理学报, 2002, 51(3): 465-467. doi: 10.7498/aps.51.465
[17]	李华兵, 黄乒花, 刘慕仁, 孔令江. 用格子Boltzmann方法模拟MKDV方程. 物理学报, 2001, 50(5): 837-840. doi: 10.7498/aps.50.837
[18]	李志斌, 潘素起. 广义五阶KdV方程的孤波解与孤子解. 物理学报, 2001, 50(3): 402-405. doi: 10.7498/aps.50.402
[19]	刘春平. 一类非线性耦合方程的孤子解. 物理学报, 2000, 49(10): 1904-1908. doi: 10.7498/aps.49.1904
[20]	张解放. 长水波近似方程的多孤子解. 物理学报, 1998, 47(9): 1416-1420. doi: 10.7498/aps.47.1416

计量

文章访问数: 8131
PDF下载量: 197
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

一个可积的逆空时非局部Sasa-Satsuma方程