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Combined Wronskian solutions to the 2D Toda molecule equation. (English) Zbl 1254.37045

Summary: By combining two pieces of bi-directional Wronskian solutions, molecule solutions in Wronskian form are presented for the finite, semi-infinite and infinite bilinear 2D Toda molecule equations. In the cases of finite and semi-infinite lattices, separated-variable boundary conditions are imposed. The Jacobi identities for determinants are the key tool employed in the solution formulations.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q51 Soliton equations
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References:

[1] Hirota, R., The Direct Method in Soliton Theory (2004), Cambridge University Press
[2] Hietarinta, J., Phys. AUC, 15, 1, 31 (2005)
[3] Ma, W. X., Phys. Lett. A, 301, 35 (2002)
[4] Ma, W. X.; Maruno, K., Physica A, 343, 219 (2004)
[5] Ma, W. X., J. Phys. Soc. Jpn., 72, 3017 (2003)
[6] Ma, W. X., Chaos Solitons Fractals, 26, 1453 (2005)
[7] Ma, W. X.; You, Y., Trans. Amer. Math. Soc., 357, 1753 (2005)
[8] Li, C. X.; Ma, W. X.; Liu, X. J.; Zeng, Y. B., Inverse Problems, 23, 279 (2007)
[9] Ma, W. X.; Li, C. X.; He, J. S., Nonlinear Anal., 70, 4245 (2009)
[10] Ma, W. X., Mod. Phys. Lett. B, 22, 1815 (2008)
[11] Ma, W. X.; Abdeljabbar, A.; Asaad, M. G., Appl. Math. Comput., 217, 10016 (2011)
[12] Ma, W. X.; Huang, T. W.; Zhang, Y., Phys. Scripta, 82, 065003 (2010)
[13] Ma, W. X.; Lee, J.-H., Chaos Solitons Fractals, 42, 1356 (2009)
[14] Ma, W. X.; Fan, E. G., Comput. Math. Appl., 61, 950 (2011)
[15] W.X. Ma, Y. Zhang, Y.N. Tang, J.Y. Tu, preprint, 2011.; W.X. Ma, Y. Zhang, Y.N. Tang, J.Y. Tu, preprint, 2011.
[16] Hirota, R.; Ito, M., J. Phys. Soc. Jpn., 52, 744 (1983)
[17] Leznov, A. N.; Saveliev, M. V., Physica D, 3, 62 (1981)
[18] Takagi, T., Lecture in Algebra (1965), Kyoritsu: Kyoritsu Tokyo
[19] Hirota, R., Progr. Theoret. Phys., 52, 1498 (1974)
[20] Hirota, R.; Ohta, Y.; Satsuma, J., Progr. Theoret. Phys. Suppl., 94, 59 (1988)
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