摘要For each non-isospectral Ablowitz–Ladik equation a strong symmetry operator is given. The strong symmetry contains time variable explicitly and by means of it two sets of symmetries are generated. Functional derivative formulae between the strong symmetry and symmetries are derived, by which the obtained symmetries are shown to compose a centerless Kac–Moody–Virasoro algebra. Master symmetries for non-isospectral Ablowitz–Ladik equations are also discussed.
Abstract：For each non-isospectral Ablowitz–Ladik equation a strong symmetry operator is given. The strong symmetry contains time variable explicitly and by means of it two sets of symmetries are generated. Functional derivative formulae between the strong symmetry and symmetries are derived, by which the obtained symmetries are shown to compose a centerless Kac–Moody–Virasoro algebra. Master symmetries for non-isospectral Ablowitz–Ladik equations are also discussed.
[1] Fokas A S 1987 Stud. Appl. Math. 77 253
[2] Zhang D J, Ning T K, Bi J B and Chen D Y 2006 Phys. Lett. A 359 458
[3] Zhang D J and Chen S T 2010 Stud. Appl. Math. 125 393
[4] Ablowitz M J and Ladik J F 1975 J. Math. Phys. 16 598
[5] Chen D Y and Zhang D J 1996 J. Math. Phys. 37 5524
[6] Ma W X and Fuchssteiner B 1999 J. Math. Phys. 40 (1999) 2400
[7] Fuchssteiner B and Fokas A S 1981 Physica D 4 47
[8] Zhang D J and Chen S T 2010 Stud. Appl. Math. 125 419
[9] Zhang D J and Chen D Y 2002 J. Phys. A: Math. Gen. 35 7225
[10] Fuchssteiner B 1983 Prog. Theor. Phys. 70 1508
2011, Vol. 28 
