BINARY NONLINEARIZATION OF THE SUPER AKNS SYSTEM

We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in the supersymmetry manifold ℝ4N|2N. The super Hamiltonian forms and integrals of motion are given explicitly.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  B. Kupershmidt,et al.  A super Korteweg-de Vries equation: An integrable system , 1984 .

[3]  Metin Gürses,et al.  A super AKNS scheme , 1985 .

[4]  Y. Manin,et al.  A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy , 1985 .

[5]  Ziemowit Popowicz,et al.  The fully supersymmetric AKNS equations , 1990 .

[6]  Yishen Li,et al.  HAMILTONIAN-STRUCTURE OF THE SUPER EVOLUTION EQUATION , 1990 .

[7]  Yi Cheng,et al.  The constraint of the Kadomtsev-Petviashvili equation and its special solutions , 1991 .

[8]  Xianguo Geng,et al.  A nonconfocal generator of involutive systems and three associated soliton hierarchies , 1991 .

[9]  B. Konopelchenko,et al.  (1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systems , 1991 .

[10]  Yi Cheng.  Constraints of the Kadomtsev-Petviashvili hierarchy , 1992 .

[11]  G. Landi,et al.  Remarks on the complete integrability of dynamical systems with fermionic variables , 1992 .

[12]  W. Oevel,et al.  Constrained KP hierarchy and bi-Hamiltonian structures , 1993 .

[13]  Wen-Xiu Ma,et al.  An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems , 1994 .

[14]  Yi Cheng.  Modifying the KP, thenth constrained KP hierarchies and their Hamiltonian structures , 1995 .

[15]  Wenxiu Ma.  Symmetry constraint of MKdV equations by binary nonlinearization , 1995 .

[16]  A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization , 1995, solv-int/9510012.

[17]  Yury J. Ionin,et al.  Problems: 10599-10605 , 1997 .

[18]  J. Shaw,et al.  Canonical gauge equivalences of the sAKNS and sTB hierarchies , 1997, solv-int/9712009.

[19]  Xing-Biao Hu,et al.  An approach to generate superextensions of integrable systems , 1997 .

[20]  L. Chau,et al.  Solving the constrained KP hierarchy by gauge transformations , 1997 .

[21]  Method of Squared Eigenfunction Potentials in Integrable Hierarchies of KP Type , 1997, solv-int/9701017.

[22]  H. Aratyn,et al.  Berezinian Construction of Super-Solitons in Supersymmetric Constrained KP Hierarchies , 1998, solv-int/9808004.

[23]  THE sAKNS HIERARCHY , 1997, solv-int/9710026.

[24]  J. Shaw,et al.  Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super KP hierarchies , 1998, solv-int/9812017.

[25]  H. Aratyn,et al.  Supersymmetric Kadomtsev-Petviashvili hierarchy: ''Ghost'' symmetry structure, reductions, and Darboux-Backlund solutions , 1998, solv-int/9801021.

[26]  Q. P. Liu,et al.  Darboux transformations for super-symmetric KP hierarchies , 2000 .

[27]  C. DeWitt-Morette,et al.  Supermanifolds: Application to supersymmetry , 2002, math-ph/0202026.

[28]  Jingsong He,et al.  Two choices of the gauge transformation for the AKNS hierarchy through the constrained KP hierarchy , 2003 .

[29]  Ruguang Zhou.  Nonlinearizations of spectral problems of the nonlinear Schrödinger equation and the real-valued modified Korteweg-de Vries equation , 2007 .

[30]  Daniel J. Velleman.  American Mathematical Monthly , 2010 .