摘要The multi-functions of soliton equation hierarchy with self-consistent sources is constructed. Then, the Jaulent-Miodek (JM) equation hierarchy with self-consistent sources is derived. Furthermore, the multi-function JM equation hierarchy with self-consistent sources is presented by using the higher-dimensional Lax pairs.
Abstract:The multi-functions of soliton equation hierarchy with self-consistent sources is constructed. Then, the Jaulent-Miodek (JM) equation hierarchy with self-consistent sources is derived. Furthermore, the multi-function JM equation hierarchy with self-consistent sources is presented by using the higher-dimensional Lax pairs.
[1] Ma W X and Fuchssteiner B 1997 Chaos Solitons Fractals 7 1227 [2] Ma W X 2000 Methods Appl. Anal. 7 21 [3] Ma W X and Fuchssteiner B 1996 Phys. Lett. A 213 49 [4] Ma W X 2003 Phys. Lett. A 316 72 [5] Ma W X 2005 J. Math. Phys. 46 033507 [6] Ma W X, Xu X X and Zhang Y F 2006 J. Math. Phys. 47 053501 [7] Ma W X, Xu X X and Zhang Y F 2006 Phys. Lett. A 351 125 [8] Guo F G and Zhang Y F 2003 J. Math. Phys. 44 5793 [9] Yu F J and Zhang H Q 2006 Phys. Lett. A 353 326 [10]Zhang Y F and Fan E G 2008 Commun. Theor. Phys. 49 845 (China) [11] Ma W X and Chen M 2006 J. Phys. A: Gen. Math. 39 10787 [12] Ablowitz M J and Clarkson P A 1991 Soliton, Nonlinear Evolution Equation and Inverse Scattering (Cambridge: Cambridge University) [13]Mel'nikov V K 1986 Phys. Lett. A 118 22 [14] Mel'nikov V K 1987 Commun. Math. Phys. 112 639 [15] Mel'nikov V K 1988 Phys. Lett. A 113 493 [16] Zeng Y B, Ma W X and Shao Y J 2001 J. Math. Phys. 42 2113 [17] Matsuno Y 1991 J. Phys. A 24 L273 [18] Hu X B 1991 J. Phys. A 24 5489 [19] Hu X B 1996 Chaos, Soliton and Fractals 7 211 [20]Zeng Y B, Ma W X and Lin R L 2000 J. Math. Phys. 41 5453 [21]Tu G Z 1989 J. Math. Phys. 33 330 [22]Lax P D 1975 Commmun. Pure Appl. Math. 28 141