N-Soliton Solutions for the Four-Potential Isopectral Ablowitz–Ladik Equation
CHEN Shou-Ting1**, ZHU Xiao-Ming1, LI Qi2, CHEN Deng-Yuan1
1Department of Mathematics, Shanghai University, Shanghai 200444 2College of Mathematics and Information Science, East China Institute of Technology, Jiangxi 310018
N-Soliton Solutions for the Four-Potential Isopectral Ablowitz–Ladik Equation
CHEN Shou-Ting1**, ZHU Xiao-Ming1, LI Qi2, CHEN Deng-Yuan1
1Department of Mathematics, Shanghai University, Shanghai 200444 2College of Mathematics and Information Science, East China Institute of Technology, Jiangxi 310018
摘要The bilinear form of the four-potential isospectral Ablowitz–Ladik (AL) equation is derived by the dependent variable transformation. The N-soliton solutions of the equation are obtained through the Hirota method. Moreover, the double Casoratian solution is found by means of the double Casoratian technique.
Abstract：The bilinear form of the four-potential isospectral Ablowitz–Ladik (AL) equation is derived by the dependent variable transformation. The N-soliton solutions of the equation are obtained through the Hirota method. Moreover, the double Casoratian solution is found by means of the double Casoratian technique.
[1] Ablowitz M J and Ladik J F 1975 J. Math. Phys. 16 598
[2] Ablowitz M J and Ladik J F 1976 J. Math. Phys. 17 1011
[3] Zhang D J and Chen D Y 2002 Chaos, Solitons & Fractals 14 573
[4] Gesztesy F et al 2008 Stud. Appl. Math. 120 361
[5] Zhang D J and Chen D Y 2002 J. Phys. A: Math. Gen. 35 7225
[6] Zeng Y B et al 1995 J. Phys. A: Math. Gen. 28 113
[7] Geng X G et al 2007 Stud. Appl. Math. 118 281
[8] Geng X G et al 2007 J. Math. Anal. Appl. 327 829
[9] Tamizhmani K M and Ma W X 2000 J. Phys. Soc. Jpn. 69 351
[10] Zhang D J et al 2006 Phys. Lett. A 359 458
[11] Zhang D J and Chen S T 2010 Stud. Appl. Math. 125 393
[12] Zhang D J and Chen S T 2010 Stud. Appl. Math. 125 419
[13] Ablowitz M J, Prinari B and Trubatch A D 2004 Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge: Cambridge University)
[14] Geng X G 1989 Acta Math. Sci. 9 21 [15] Li Q 2011 Double Casoratian solutions of the Ablowitz–Ladik equation (in preparation)
[16] Freeman N C and Nimmo J J C 1983 Phys. Lett. A 95 1
[17] Gegenhasi et al 2006 Inverse Problems 22 1677
[18] Wu H and Zhang D J 2003 J Phys A: Gen Math. 36 4867
2011, Vol. 28 
