Binary constrained flows and separation of variables for soliton equations

ANZIAM Journal

Volumn 44, Issue 1, 2002, Pages 129-139

  Ma, Wen Xiu ^a   Zeng, Yunbo ^b  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005234093     PISSN: 14461811     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1446181100007987     Document Type: Article

References (18)

1. M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, "The inverse scattering transform - Fourier analysis for nonlinear problems", Studies in Appl. Math. 53 (1974) 249-315.
2. M. Antonowicz and S. Rauch-Wojciechowski, "Soliton hierarchies with sources and Lax representation for restricted flows", Inverse Problems 9 (1993) 201-215.
3. B. A. Dubrovin, "Theta-functions and nonlinear equations", Russian Math. Survey 36 (1981) 11-92.
4. J. C. Eilbeck, V. Z. Enol'skii, V. B. Kuznetsov and A. V. Tsiganov, "Linear r-matrix algebra for classical separable systems", J. Phys. A: Math. Gen. 27 (1994) 567-578.
5. +* and separation of variables". Commun. Math. Phys. 172 (1995) 263-285.
6. P. P. Kulish, S. Rauch-Wojciechowski and A. V. Tsiganov, "Stationary problems for equation of the KdV type and dynamical r-matrices", J. Math. Phys. 37 (1996) 3463-3482.
7. V. B. Kuznetsov, "Quadrics on real Riemannian spaces of constant curvature: separation of variables and connection with Gaudin magnet", J. Math. Phys. 33 (1992) 3240-3254.
8. Y. Li and W. X. Ma, "Binary linearization of AKNS spectral problem under higher-order symmetry constraints", Chaos, Solitons and Fractals 11 (2000) 697-710.
9. W. X. Ma, "New finite-dimensional integrable systems by symmetry constraint of the KdV equations", J. Phys. Soc. Jpn. 64 (1995) 1085-1091.
10. W. X. Ma, "Symmetry constraint of MKdV equations by binary nonlinearization", Physica A219 (1995) 467-481.
11. W. X. Ma and B. Fuchssteiner, "Binary linearization of the Lax pairs", in Nonlinear Physics (eds. E. Alfinito, M. Boiti, L. Martina and F. Pempinelli), (World Scientific, Singapore, 1996) 217-224.
12. W. X. Ma, B. Fuchssteiner and W. Oevel, "A 3 × 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization", Physica A233 (1996) 331-354.
13. W. X. Ma and W. Strampp, "An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems", Phys. Lett. A185 (1994) 277-286.
14. E. K. Sklyanin, "Separation of variables-new trends. Quantum field theory, integrable models and beyond". Prog. Theor. Phys. Suppl. 118 (1995) 35-60.
15. Y. Zeng, "Separation of variables for the constrained flows", J. Math. Phys. 38 (1997) 321-329.
16. Y. Zeng, "Using factorization to solve soliton equations", J. Phys. A: Math. Gen. 30 (1997) 3719-3724.
17. Y. Zeng and Y. Li, "The deduction of the Lax representation for constrained flows from the adjoint representation", J. Phys. A: Math. Gen. 26 (1993) L273-L278.
18. Y. Zeng and W. X. Ma, "Separation of variables for soliton equations via their binary constrained flows", J. Math. Phys. 40 (1999) 6526-6557.