修正离散KP系列的流方程
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摘要
该文主要研究修正离散KP系列的流方程问题,给出流方程的一般表示形式.
In this paper, we mainly study the flow equations of the modified discrete KP hierarchy, and derive a general formula of the flow equation.
In this paper, we mainly study the flow equations of the modified discrete KP hierarchy, and derive a general formula of the flow equation.
引文
[1] Haine L, Iliev P. Commutative. Lax pairs, symmetries and an Adilic flag manifold. Int Math Res Not,2000, 6:281-323
[2] Kupershimidt B A. Discrete Lax equations and difference calculus. Asterisque, 1985, 123:1-212
[3] Li M H, He J S. The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy.Commun Nonlin Sci Numer Simulat, 2016, 34:210-223
[4] Liu S W, Ma W X. The string aquation and the-r-function witt constraints for the discrete KadomtsevPetviashvili hierarchy. J Math Phys, 2013, 54:103513
[5] Liu S W, Cheng Y, He J S. The determinant representtion of the gauge transformation for the discrete KP hierarchy. Sci China Math, 2010, 53:1195-1206
[6] Li M H, Cheng J P, He J S. The gauge transformation of the constrained semi-discrete KP hierarchy. Mod Phys Lett B, 2013, 27:1350043
[7] Cheng J P, Li M H, He J S. The Virasoro a-ction on the tau function for the constrained discrete KP hierarchy. J Nonlin Math Phys, 2013, 20:529-538
[8] Li M H, Cheng J P, He J S. The compatibility of additional symmetry and geuge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy. J Nonlin Math Phys, 2015, 22:17-31
[9] Liu S W, Cheng Y. Sato B(a|¨)cklund transformation, additional symmetries and ASvM formula for the discrete KP hierarchy. J Phys A:Math Theor, 2010, 43:135202
[10] Li M H, Tian K L, He J S, et al. Virasoro type algebraic structure hidden in the constrained discrete KP hierarchy. J Math Phys, 2013, 54:043512
[11] Oevel W. Darboux transformations for integrable lattice systems//Alfinito E, Boiti M, Martina L, et al.Nonlinear Physics:Theory and Experiment. Singapore:World Scientific, 1996:233-240
[12] Tamizhmani K M, Kanaga Vel S. Gauge equivalence and t-reductions of the differential-difference KP equation. Chaos Soliton Fract, 2000, 11:137-143
[13] Li M H, Cheng J P, He J S. The successive application of the gauge transformation for the modified semidiscrete KP hierarchy. Z Naturforsch A, 2016, 71:1093-1098
[14] Huang R, Song T, Li C Z. Gauge transformations of constrained discrete modified KP systems with self-consistent sources. Inter J Geom Meth Mod Phys, 2017, 14:1750052
[15] Zhang D J, Wu H, Deng S F, et al. General formulae for two pseudo-differential operaters. Commun Theor Phys, 2008, 49:1393-1396
[16] Zhang D J, Chen D Y. Addendum to “some general formulas in the Sato theory”. J Phys Soc Jpn, 2003,72:2130-2131
[17] Zhang D J, Chen D Y. Some general formulas in the Sato theory. J Phys Soc Jpn, 2003, 72:448-449
[18] Cheng J P, He J S, Wang L H. A general formula of flow equations for Harry-Dym hierarchy. Commun Theor Phys, 2011, 55:193-198
[2] Kupershimidt B A. Discrete Lax equations and difference calculus. Asterisque, 1985, 123:1-212
[3] Li M H, He J S. The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy.Commun Nonlin Sci Numer Simulat, 2016, 34:210-223
[4] Liu S W, Ma W X. The string aquation and the-r-function witt constraints for the discrete KadomtsevPetviashvili hierarchy. J Math Phys, 2013, 54:103513
[5] Liu S W, Cheng Y, He J S. The determinant representtion of the gauge transformation for the discrete KP hierarchy. Sci China Math, 2010, 53:1195-1206
[6] Li M H, Cheng J P, He J S. The gauge transformation of the constrained semi-discrete KP hierarchy. Mod Phys Lett B, 2013, 27:1350043
[7] Cheng J P, Li M H, He J S. The Virasoro a-ction on the tau function for the constrained discrete KP hierarchy. J Nonlin Math Phys, 2013, 20:529-538
[8] Li M H, Cheng J P, He J S. The compatibility of additional symmetry and geuge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy. J Nonlin Math Phys, 2015, 22:17-31
[9] Liu S W, Cheng Y. Sato B(a|¨)cklund transformation, additional symmetries and ASvM formula for the discrete KP hierarchy. J Phys A:Math Theor, 2010, 43:135202
[10] Li M H, Tian K L, He J S, et al. Virasoro type algebraic structure hidden in the constrained discrete KP hierarchy. J Math Phys, 2013, 54:043512
[11] Oevel W. Darboux transformations for integrable lattice systems//Alfinito E, Boiti M, Martina L, et al.Nonlinear Physics:Theory and Experiment. Singapore:World Scientific, 1996:233-240
[12] Tamizhmani K M, Kanaga Vel S. Gauge equivalence and t-reductions of the differential-difference KP equation. Chaos Soliton Fract, 2000, 11:137-143
[13] Li M H, Cheng J P, He J S. The successive application of the gauge transformation for the modified semidiscrete KP hierarchy. Z Naturforsch A, 2016, 71:1093-1098
[14] Huang R, Song T, Li C Z. Gauge transformations of constrained discrete modified KP systems with self-consistent sources. Inter J Geom Meth Mod Phys, 2017, 14:1750052
[15] Zhang D J, Wu H, Deng S F, et al. General formulae for two pseudo-differential operaters. Commun Theor Phys, 2008, 49:1393-1396
[16] Zhang D J, Chen D Y. Addendum to “some general formulas in the Sato theory”. J Phys Soc Jpn, 2003,72:2130-2131
[17] Zhang D J, Chen D Y. Some general formulas in the Sato theory. J Phys Soc Jpn, 2003, 72:448-449
[18] Cheng J P, He J S, Wang L H. A general formula of flow equations for Harry-Dym hierarchy. Commun Theor Phys, 2011, 55:193-198