(3+1)维Burgers系统的瞬内嵌孤子和瞬锥形孤子

马松华; 方建平; 任清褒

doi:10.7498/aps.59.4420

摘要

利用投射方程法和变量分离法,得到了(3+1)维Burgers系统的变量分离解(包括孤波解、周期波解和有理函数解).根据孤波解和有理函数解,构造出Burgers系统新颖的局域结构,例如瞬内嵌孤子和瞬锥形孤子.

关键词:

With a projective equation method and a variable separation method, new families of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) for (3+1)-dimensional Burgers system is derived. Based on a derived solitory wave solution and a rational function solution, we obtain some novel localized structures such as instantaneous embed soliton and instantaneous taper-like soliton.

Keywords:

作者及机构信息

1.
丽水学院物理系,丽水 323000

基金项目: 浙江省自然科学基金(批准号:Y6090545,Y606252)和丽水学院自然科学基金(批准号:KZ09005)资助的课题.

Authors and contacts

1.
Department of Physics, Lishui University, Lishui 323000, China

参考文献

[1]	Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2]	Kivshar Y S, Melonmend B A 1989 Rev. Mod. Phys. 61 765
[3]	Kadomtsev B B, Petviashvili V I 1970 Sov. Phys. Dokl. 15 539
[4]	Davey A, Stewartson K 1974 Proc. Roy. Soc. 338 17
[5]	Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[6]	Lou S Y 1998 Phys. Rev. Lett. 80 5027
[7]	Zhang J F, Huang W H, Zheng C L 2002 Acta Phys. Sin. 51 2676 (in Chinese) [张解放、黄文华、郑春龙2002 512676]
[8]	Zhang D J 2003 Chaos Soliton. Fract. 18 31
[9]	Zhang D J 2005 Chaos soliton. Fract. 23 1333
[10]	Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[11]	Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[12]	Lou S Y 1999 Sci. China 42 537 (in Chinese) [楼森岳1999中国科学42537]
[13]	Zheng C L, Zhang J F 2002 Acta Phys. Sin. 51 2426 (in Chinese) [郑春龙、张解放2005 512426]
[14]	Zheng C L, Fang J P, Chen L Q 2005 Acta Phys. Sin. 54 1468 (in Chinese) [郑春龙、方建平、陈立群2005 541468]
[15]	Zhu J M, Ma Z Y, Zheng C L 2004 Acta Phys. Sin. 53 3248 (in Chinese) [朱加民、马正义、郑春龙2004 533248]
[16]	Lou S Y 1995 J. Phys. Math. Gen. A 28 7227
[17]	Ruan H Y, Lou S Y 1997 J. Math. Phys. 38 3123
[18]	Ma Z Y, Zhu J M, Zheng C L 2004 Chin. Phys. 9 1382
[19]	Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[20]	Lou S Y 1996 Commun. Theor. 26 487
[21]	Lou S Y, Ruan H Y 2001 J.Phys. A 34 305
[22]	Lai D W C, Chou K W 1999 J. Phys. Soc. Jpn. 65 1847
[23]	Mo J Q 2009 Acta Phys. Sin. 58 0695 (in Chinese) [莫嘉珙2009 580695]
[24]	Liang L W, Li X D, Li Y X 2009 Acta Phys. Sin. 58 2159 (in Chinese) [梁立为、李兴东、李玉霞2009 582159]
[25]	Lou S Y 2000 Phys. Lett. A 277 94
[26]	Tang X Y, Liang Z F 2006 Phys. Lett. A 351 398
[27]	Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448
[28]	Fang J P, Zheng C L, Zhu J M 2005 Commun. Theor. Phys. 44 203
[29]	Ma S H, Wu X H, Fang J P, Zheng C L 2006 Z. Naturforsch. 61 a 249
[30]	Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 0620 (in Chinese) [马松华、强继业、方建平2007 560620]
[31]	Fang J P, Zheng C L 2005 Chin. Phys. 14 670
[32]	Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平、郑春龙、朱加民2005 542990]
[33]	Huang L, Sun J A, Dou F Q, Duan W S, Liu X X 2007 Acta Phys. Sin. 56 0611 (in Chinese) [黄磊、孙建安、豆福全、段文山、刘兴霞2007 560611]
[34]	Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华、方建平2006 555611]
[35]	Ma S H, Fang J P, Hong B H, Zheng C L 2009 Chaos Soliton. Fract. 40 1352
[36]	Ma S H, Fang J P, Zheng C L 2008 Z. Naturforsch. 63 a 121
[37]	Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[38]	Lou S Y, Yu J, Tang X Y 2000 Z. Naturforsch. 55 a 867
[39]	Dai C Q, Yan C J, Zhang J F 2006 Commun. Theor. Phys. 46 389
[40]	Kong F L, Chen S D 2006 Chaos Soliton. Fract. 27 495

施引文献

[1]	Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2]	Kivshar Y S, Melonmend B A 1989 Rev. Mod. Phys. 61 765
[3]	Kadomtsev B B, Petviashvili V I 1970 Sov. Phys. Dokl. 15 539
[4]	Davey A, Stewartson K 1974 Proc. Roy. Soc. 338 17
[5]	Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[6]	Lou S Y 1998 Phys. Rev. Lett. 80 5027
[7]	Zhang J F, Huang W H, Zheng C L 2002 Acta Phys. Sin. 51 2676 (in Chinese) [张解放、黄文华、郑春龙2002 512676]
[8]	Zhang D J 2003 Chaos Soliton. Fract. 18 31
[9]	Zhang D J 2005 Chaos soliton. Fract. 23 1333
[10]	Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[11]	Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[12]	Lou S Y 1999 Sci. China 42 537 (in Chinese) [楼森岳1999中国科学42537]
[13]	Zheng C L, Zhang J F 2002 Acta Phys. Sin. 51 2426 (in Chinese) [郑春龙、张解放2005 512426]
[14]	Zheng C L, Fang J P, Chen L Q 2005 Acta Phys. Sin. 54 1468 (in Chinese) [郑春龙、方建平、陈立群2005 541468]
[15]	Zhu J M, Ma Z Y, Zheng C L 2004 Acta Phys. Sin. 53 3248 (in Chinese) [朱加民、马正义、郑春龙2004 533248]
[16]	Lou S Y 1995 J. Phys. Math. Gen. A 28 7227
[17]	Ruan H Y, Lou S Y 1997 J. Math. Phys. 38 3123
[18]	Ma Z Y, Zhu J M, Zheng C L 2004 Chin. Phys. 9 1382
[19]	Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[20]	Lou S Y 1996 Commun. Theor. 26 487
[21]	Lou S Y, Ruan H Y 2001 J.Phys. A 34 305
[22]	Lai D W C, Chou K W 1999 J. Phys. Soc. Jpn. 65 1847
[23]	Mo J Q 2009 Acta Phys. Sin. 58 0695 (in Chinese) [莫嘉珙2009 580695]
[24]	Liang L W, Li X D, Li Y X 2009 Acta Phys. Sin. 58 2159 (in Chinese) [梁立为、李兴东、李玉霞2009 582159]
[25]	Lou S Y 2000 Phys. Lett. A 277 94
[26]	Tang X Y, Liang Z F 2006 Phys. Lett. A 351 398
[27]	Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448
[28]	Fang J P, Zheng C L, Zhu J M 2005 Commun. Theor. Phys. 44 203
[29]	Ma S H, Wu X H, Fang J P, Zheng C L 2006 Z. Naturforsch. 61 a 249
[30]	Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 0620 (in Chinese) [马松华、强继业、方建平2007 560620]
[31]	Fang J P, Zheng C L 2005 Chin. Phys. 14 670
[32]	Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平、郑春龙、朱加民2005 542990]
[33]	Huang L, Sun J A, Dou F Q, Duan W S, Liu X X 2007 Acta Phys. Sin. 56 0611 (in Chinese) [黄磊、孙建安、豆福全、段文山、刘兴霞2007 560611]
[34]	Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华、方建平2006 555611]
[35]	Ma S H, Fang J P, Hong B H, Zheng C L 2009 Chaos Soliton. Fract. 40 1352
[36]	Ma S H, Fang J P, Zheng C L 2008 Z. Naturforsch. 63 a 121
[37]	Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[38]	Lou S Y, Yu J, Tang X Y 2000 Z. Naturforsch. 55 a 867
[39]	Dai C Q, Yan C J, Zhang J F 2006 Commun. Theor. Phys. 46 389
[40]	Kong F L, Chen S D 2006 Chaos Soliton. Fract. 27 495

[1]	杨佳奇, 刘文军. 基于变系数3+1维三次-五次复金兹堡-朗道方程的亮孤子及混合孤子传输特性. , 2023, 72(10): 100504. doi: 10.7498/aps.72.20222430
[2]	张丽香, 刘汉泽, 辛祥鹏. 广义（3+1）维Zakharov-Kuznetsov方程的对称约化、精确解和守恒律. , 2017, 66(8): 080201. doi: 10.7498/aps.66.080201
[3]	许永红, 姚静荪, 莫嘉琪. (3+1)维Burgers扰动系统孤波的解法. , 2012, 61(2): 020202. doi: 10.7498/aps.61.020202
[4]	蒋黎红, 马松华, 方建平, 吴红玉. (3+1)维Burgers系统的新孤子解及其演化. , 2012, 61(2): 020510. doi: 10.7498/aps.61.020510
[5]	曾文丽, 马松华, 任清褒. (2+1)维 Bogoyavlenskii-Schiff 系统的精确解和孤子激发. , 2012, 61(11): 110508. doi: 10.7498/aps.61.110508
[6]	雷军, 马松华, 方建平. (3+1)维Jimbo-Miwa方程的精确解及局域激发. , 2011, 60(12): 120507. doi: 10.7498/aps.60.120507
[7]	雷军, 马松华, 方建平. (2+1)维破裂孤子方程的多方孤子解及其混沌行为. , 2011, 60(5): 050302. doi: 10.7498/aps.60.050302
[8]	温朝晖, 莫嘉琪. 广义(3+1)维非线性Burgers系统孤波级数解. , 2010, 59(12): 8311-8315. doi: 10.7498/aps.59.8311
[9]	吴勇旗. 一个（3+1）维孤子方程的周期解. , 2010, 59(1): 54-59. doi: 10.7498/aps.59.54
[10]	周振春, 马松华, 方建平, 任清褒. (2+1)维孤子系统的多孤子解和分形结构. , 2010, 59(11): 7540-7545. doi: 10.7498/aps.59.7540
[11]	马松华, 吴小红, 方建平, 郑春龙. (3+1)维Burgers系统的新精确解及其特殊孤子结构. , 2008, 57(1): 11-17. doi: 10.7498/aps.57.11
[12]	何宝钢, 徐昌智, 张解放. 扩展的形变映射方法和(2+1)维破裂孤子方程的新解. , 2006, 55(2): 511-516. doi: 10.7498/aps.55.511
[13]	沈守枫. (1+1)维广义的浅水波方程的变量分离解和孤子激发模式. , 2006, 55(3): 1016-1022. doi: 10.7498/aps.55.1016
[14]	曾昕, 张鸿庆. (2+1)维色散长波方程的新的类孤子解. , 2005, 54(2): 504-510. doi: 10.7498/aps.54.504
[15]	何宝钢, 徐昌智, 张解放. (2+1)维非线性KdV方程的新孤子结构. , 2005, 54(12): 5525-5529. doi: 10.7498/aps.54.5525
[16]	张解放, 郭冠平. (2+1)维破裂孤子方程的新多孤子解. , 2003, 52(10): 2359-2362. doi: 10.7498/aps.52.2359
[17]	李画眉. (3+1)维Nizhnik-Novikov-Veselov方程的孤子解和周期解. , 2002, 51(3): 465-467. doi: 10.7498/aps.51.465
[18]	阮航宇, 陈一新. (2+1)维非线性薛定谔方程的环孤子,dromion,呼吸子和瞬子. , 2001, 50(4): 586-592. doi: 10.7498/aps.50.586
[19]	范恩贵, 张鸿庆. 非线性孤子方程的齐次平衡法. , 1998, 47(3): 353-362. doi: 10.7498/aps.47.353
[20]	海文华, 肖奕. 微扰Burgers-KdV方程的孤子解. , 1996, 45(4): 587-594. doi: 10.7498/aps.45.587

计量

文章访问数: 7493
PDF下载量: 929
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