Adjoint Symmetry Constraints Leading to Binary Nonlinearization

References

• Ma , W X and Strampp , W . 1994 . An Explicit Symmetry Constraint for the Lax Pairs and the Adjoint Lax Pairs of AKNS Systems . Phys. Lett. , A 185 : 277 – 286 .
   Web of Science ®Google Scholar
• Ma , W X . 2001 . Binary Bargmann Symmetry Constraints of Soliton Equations, in Proceedings of the Third World Congress of Nonlinear Analysts . Nonlinear Analysis , 47 : 5199 – 5211 .
   Web of Science ®Google Scholar
• Cao , C W and Geng , X G . 1990 . “ Classical integrable systems generated through nonlinearization of eigenvalue problems ” . In Nonlinear Physics , Edited by: Gu , C H , Li , Y S and Tu , G Z . 68 – 78 . Berlin : Springer .
   Google Scholar
• Ma , W X . 1990 . “ The Confocal Involutive System and the Integrability of the Nonlinearized Lax Systems of AKNS Hierarchy ” . In Nonlinear Physics , Edited by: Gu , C H , Li , Y S and Tu , G Z . 79 – 84 . Berlin : Springer .
   Google Scholar
• Zeng , Y B and Ma , W X . 1999 . Separation of Variables for Soliton Equations via Their Binary Constrained Flows . J. Math. Phys. , 40 : 6526 – 6557 .
   Web of Science ®Google Scholar
• Ma W X Zeng Y B Binary Constrained Flows and Separation of Variables for Soliton Equations, in Proceedings of the Conference on Integrable Systems, in celebration of Martin D. Kruskal’s 75th Birthday, Adelaide, Australia, (2000) to appear
   Google Scholar
• Ma , W X . 1995 . Symmetry Constraint of MKdV Equations by Binary Nonlinearization . Physica A , 219 : 467 – 481 .
   Google Scholar
• Ma , W X and Zhou , Z X . 2001 . Binary Symmetry Constraints of N -wave Interaction Equations in 1+1 and 2+1 Dimensions . J. Math. Phys. , 42 : 4345 – 4382 .
   Web of Science ®Google Scholar
• Ma W X Geng X G Bäcklund Transformations of Soliton Systems from Symmetry Constraints, in Proceedings of the Workshop on Bäcklund & Darboux Transformations, Halifax, Canada, 1999, to appear
   Google Scholar
• Xu , X X . 1995 . New Finite-dimensional Integrable Systems by Binary Nonlinearization of WKI Equations . Chinese Phys. Lett. , 12 : 513 – 516 .
   Web of Science ®Google Scholar
• Ma , W X , Ding , Q , Zhang , W G and Lu , B G . 1996 . Binary Nonlinearization of Lax Pairs of Kaup-Newell Soliton Hierarchy . Il Nuovo Cimento B , 111 : 1135 – 1149 .
   Google Scholar
• Ma , W X , Fuchssteiner , B and Oevel , W . 1996 . A 3 × 3 Matrix Spectral Problem for AKNS Hierarchy and Its Binary Nonlinearization . Physica A , 233 : 331 – 354 .
   Google Scholar
• Ma , W X and Fuchssteiner , B . 1996 . “ Binary Nonlinearization of Lax Pairs ” . In Nonlinear Physics: Theory and Experiment , Edited by: Alfinito , E , Boiti , M , Martina , L and Pempinelli , F . 217 – 224 . River Edge , NJ : World Scientific .
   Google Scholar
• Ablowitz , M J , Kaup , D J , Newell , A C and Segur , H . 1974 . The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems . Stud. Appl. Math. , 53 : 249 – 315 .
   Web of Science ®Google Scholar
• Ma W X Some aspects of nonlinear integrable systems, Ph.D. dissertation, Academia Sinica, Beijing, China, 1990
   Google Scholar
• Tu , G Z . 1989 . The Trace Identity, a Powerful Tool for Constructing the Hamiltonian Structure of Integrable Systems . J. Math. Phys. , 30 : 330 – 338 .
   Web of Science ®Google Scholar
• Fuchssteiner , B and Fokas , A C . 1981/82 . Symplectic Structures, Their Bäcklund Transformations and Hereditary Symmetries . Physica D , 4 : 47 – 66 .
   Web of Science ®Google Scholar
• Ablowitz , M J and Haberman , R . 1975 . Resonantly Coupled Nonlinear Evolution Equations . J. Math. Phys. , 16 : 2301 – 2305 .
   Web of Science ®Google Scholar
• Kaup , D J . 1976 . The Three-wave Interaction - a Nondispersive Phenomenon . Stud. Appl. Math. , 55 : 9 – 44 .
   Web of Science ®Google Scholar
• Wu , Y T and Geng , X G . 1999 . A Finite-dimensional Integrable System Associated with the Three-wave Interaction Equations . J. Math. Phys. , 40 : 3409 – 3430 .
   Web of Science ®Google Scholar
• Li , Y S and Ma , W X . 2000 . Binary Nonlinearization of AKNS Spectral Problem under Higher-order Symmetry Constraints . Chaos, Solitons and Fractals , 11 : 697 – 710 .
   Web of Science ®Google Scholar
• Ma , W X and Zhou , R G . 2001 . Nonlinearization of Spectral Problems for the Perturbation KdV Systems . Physica A , 296 : 60 – 74 .
   Web of Science ®Google Scholar