摘要Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4×4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al.(e-print arXiv:0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.
Abstract：Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4×4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al.(e-print arXiv:0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.
[1] Hirota R and Satsuma J 1981 Phys. Lett. A 85 407
[2] Satsuma J and Hirota R 1982 J. Phys. Soc. Jpn. 51 3390
[3] Dodd R and Fordy A 1982 Phys. Lett. A 89 168
[4] Ito M 1982 Phys. Lett. A 91 335
[5] Foursov M V 2000 Inverse Probl. 16 259
[6] Svinolupov S I 1992 Commun. Math. Phys. 143 559
[7] Habibullin I T and Svinolupov S I 1995 Physica D 87 134
[8] Wadati M and Tsuchida N 2006 J. Phys. Soc. Jpn. 75 014301
[9] Gear J A 1985 Stud. Appl. Math. 72 95
[10] Brazhnyi V A and Konotop V V 2005 Phys. Rev. E 72 026616
[11] Lou S Y et al 2006 J. Phys. A: Math. Gen. 39 513
[12] Lou S Y, Tong B, Jia M and Li J H arXiv:0711.0420
[13] Liu P and Lou S Y 2010 Chin. Phys. Lett. 27 020202
[14] Brazhnyi V A et al 2005 Phys. Rev. E 72 026616
[15] Sahadevana R and Balakrishnan S 2008 J. Math. Phys. 49 113510
[16] Zhao H Q and Zhu Z N 2011 J. Math. Phys. 52 023512
[17] Tu G Z 1990 J. Phys. A: Math. Gen. 23 3903
2011, Vol. 28 
