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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.
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Keywords:
- projective equation method /
- (3+1)-dimensional Burgers system /
- instantaneous embed soliton /
- instatntaneous taper-like soliton
[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] 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
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