Abstract
We consider generalizedk-constraints of the KP hierarchy where the Lax operatorL is forced to satisfy L k− =q∂−1r. We study the effect of those constraints on the bilinear equations.
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Ohta, Y., Satsuma, J., Takahashi, D., and Tokihiro, T.:Prog. Theor. Phys. Suppl. 94 (1988), 219.
Date, E., Jimbo, M., Kashiwara, M., and Miwa, T.: in M. Jimbo and T. Miwa (eds),Nonlinear Integrable Systems — Classical and Quantum Theory, World Scientific, Singapore, 1983, pp. 39; Jimbo, M. and Miwa, T.:Publ. RIMS, Kyoto Univ. 19 (1983), 943.
Cheng, Y. and Li, Y. S.:Phys. Lett. A 157 (1991), 22;J. Phys. A 25 (1992), 419.
Konopelchenko, B. G. and Strampp, W.:Inverse Problems 7 (1991), L17;J. Math. Phys. 33 (1992), 3676.
Konopelchenko, B. G., Sidorenko, J., and Strampp, W.:Phys. Lett. A 157 (1991), 17.
Sidorenko, J. and Strampp, W.:Inverse Problems 7 (1991), L37.
Xu, B.:Inverse Problems 8 (1992), L13; (1 + 1)-dimensional integrable Hamiltonian systems reduced from the KP hierarchy,Inverse Problems 9 (1993), 355.
Cheng, Y.:J. Math. Phys. 33 (1992), 3774.
Xu, B. and Li, Y.:J. Phys. A 25 (1992), 2957.
Sidorenko, J. and Strampp, W.: Multicomponent integrable reductions in the KP hierarchy, Preprint (1991);J. Math. Phys. 34 (1993), 1429.
Oevel, W. and Strampp, W.: Constrained KP hierarchy and bi-Hamiltonian structures,Comm. Math. Phys. 157 (1993), 51.
Lebedev, D., Orlov, A., Pakuliak, S., and Zabrodin, A.:Phys. Lett. A 160 (1991), 166.
Cheng, Y. and Zhang, Y.-J.: Bilinear equations for the constrained KP hierarchy, Preprint, Hefei University, 1992.
Cheng, Y, Strampp, W., and Zhang, Y.-J.: Bilinear Bäcklund transformations for the KP and k-constrained KP hierarchy, Preprint, Hefei University, 1993.
Matsukidaira, J., Satsuma, J., and Strampp, W.:Phys. Lett. A 147 (1990), 467.
Satsuma, J., Matsukidaira, J., and Kajiwara, K.: in I. Antoniou and F. J. Lambert (eds),Solitons and Chaos, Springer-Verlag, Berlin, 1991, pp. 264–269.
Hietarinta, J., Kajiwara, K., Matsukidaira, J., and Satsuma, J.: in M. Boiti, L. Martina and F. Pempinelli (eds),Nonlinear Evolution Equations and Dynamical Systems, World Scientific, Singapore, 1992, pp. 30–43.
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Cheng, Y., Zhang, YJ. & Strampp, W. Constraints of the KP hierarchy and the bilinear method. Acta Appl Math 41, 341–348 (1995). https://doi.org/10.1007/BF00996122
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DOI: https://doi.org/10.1007/BF00996122