Symmetries, exact solutions and conservation laws of Caudrey–Dodd–Gibbon–Kotera–Sawada equation

Abstract

Abstract:

By using the improved CK´s, the symmetry group theorem (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation was derived. Some new exact solutions of (2+1)-dimensional CDGKS equation are obtained by applying our theorem and given solutions, which expands the scope of the solutions of CDGKS equation. Infinite conservation laws of (2+1)-dimensional CDGKS equation are also found by symmetries and the adjoint equation.

Key words: (2+1)-dimensional CDGKS equation, improved CK´s, exact solutions, conservation laws

CLC Number:

O175.2

WANG Ting-ting, LIU Xi-qiang, YU Jin-qian. Symmetries, exact solutions and conservation laws of Caudrey–Dodd–Gibbon–Kotera–Sawada equation[J]. J4, 2011, 28(4): 385-390.

References

[1] Konopelchenko, B., Dubrovsky, V.. Some new integrable evolution equations in 2+1 dimensions [J]. Phys. Lett. A, 1984, 102: 15-17.
[2] Yi Cheng, Yi-Shen Li. J. Phys. Constraints of the 2+1 dimensional integrable soliton systems [J]. J. Phys. A: Math. Gen., 1992, 25: 419.
[3] Chan W. L., Zheng Yu-Kun. Backlund transformations for the Caudrey–Dodd–Gibbon–Kotera–
Sawada equation and itsλ-modified equation [J]. J. Math. Phys., 1989, 30; 2065-2068.
[4] Cao Ce-wen, Wu Yong-tang, Geng Xian-guo. On quasi-periodic solutions of the 2+1 dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation [J]. Phys. Lett. A, 1999, 256: 59–65.
[5] Lv Na, Mei Jian-Qin, Zhang Hong-Qing. Symmetry Reductions and Group-Invariant Solutions of (2+1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation [J]. Commun. Theor. Phys., 2010, 53: 591-596.
[6] J.D. Gibbon, R.K. Dodd, P.J. Caudrey. A new hierarchy of Kortewge-de Vries equations [J]. Proc. Roy. Soc. Lond. Ser. A., 1976, 351: 407-422.
[7] R.K. Dodd, J.D. Gibbon. The prolongation structure of a higher order Kortewge-de Vries equations [J]. Proc. Roy. Soc. Lond. Ser. A., 1977, 358: 287-296.
[8] Lou Sen-Yue, Ma Hong-Cai. Non-Lie symmetry groups of (2+1) –dimensional nonlinear systems obtained form a simple direct method [J]. J. Phys A: Math. Gen. 2005, 38: L129~L137.
[9] Gao Jie, Liu Xi-Qiang, Guo Mei-Yu. New solutions and conservation lows of the (3+1)-dimensional nonlinear evolution equations [J]. Chinese Journal of Quantum Electronics(量子电子学报), 2009, (1): 16-22 (in Chinese).
[10] Yang Zong-Hang. A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation [J]. Commun. Theor. Phys., 2006, 46: 807-811.
[11] Xu Bin, Liu Xi-Qiang. Symmetry reduction and invariable solutions of the (2+1)-dimensional Gardner equation [J]. Chinese Journal of Quantum Electronics(量子电子学报). 2009, 26(5): 531-536(in Chinese).
[12] Nail H I. A new conservation theorem [J]. J. Math. Anal. Appl., 2007, 333: 311~328.

[1]	MA Zhi-min 1，*， SUN Yu-huai 2. The new exact solutions of cubic nonlinear schr\"{o}dinger equations [J]. Chinese Journal of Quantum Electronics, 2019, 36(4): 416-422.
[2]	. New exact solutions of the Brinkman model describing the natural convection in porous media [J]. J4, 2017, 34(6): 691-699.
[3]	Wang Xiao-li, Sirendaoerji. Exp-Expansion Method and Exact Solutions of Two Variable Coefficients Nonlinear Evolution Equations [J]. J4, 2016, 33(6): 680-688.
[4]	. Lie symmetry analysis and exact solutions for nonlinear LC circuit equation [J]. J4, 2016, 33(3): 279-286.
[5]	LI Kang, LIU Xi-qiang. Explicit solutions of the generalized Kuramoto-Sivashinsky equation with variable coefficients [J]. J4, 2015, 32(4): 419-424.
[6]	JIN Linghua, PANG Jing. Generalized Solution of Variant Boussinesq Equations [J]. J4, 2015, 32(4): 425-430.
[7]	FENG Chun-ming，LIU Qing-song. Symmetries, reductions, exact solutions and conservation laws of the Zabolotskaya-KhokhlovEquation with a Dissipative Term [J]. J4, 2015, 32(1): 46-52.
[8]	YU Xingjiang. Symmetries, reductions and exact solutions of KdV-Zakharov-Kuznetsev equation [J]. J4, 2014, 31(6): 670-677.
[9]	Liu Yong，Liu Xi-Qiang，Wang Zhen-Li. Symmetries, reductions and exact solutions of (2+1) dimensional Potential Boiti-Leon-Manna-Pempinelli equation [J]. J4, 2014, 31(5): 533-540.
[10]	Wang Zhen-li, Liu Xi-qiang. Symmetry reduction and exact solutions of a generalized fourth-order dispersive equation [J]. J4, 2014, 31(3): 264-272.
[11]	KANG Xiao-rong,XIAN Da-quan. Symmetry reduction and new non-traveling wave solutions of (2+1)-dimensional AKNS equation [J]. J4, 2013, 30(6): 678-683.
[12]	. Nonlinear self-adjointness and conservation laws of forced KdV equation [J]. J4, 2013, 30(2): 154-161.
[13]	YANG Li-juan， YANG Qiong-fen，DU Xian-yun. New exact solutions of Broer–Kaup–Kupershmidt equation [J]. J4, 2012, 29(2): 142-146.
[14]	Chen Mei，Liu Xiqiang，Wang Meng. Exact solutions and conservation laws of Symmetric Regularized Long Wave(SRLW) equations [J]. J4, 2012, 29(1): 21-26.