[1] Zabusky N J, Kruskal M D[J]. Phys. Rev. Lett., 15, 240(1965).
[2] Gardner C S, Greene J M, Kruskal M D, Miura R M[J]. Phys. Rev. Lett., 19, 1095(1967).
[3] Lax P D[J]. Commun. Pure Appl. Math., 21, 467(1968).
[4] Deift P[J]. arXiv: 1902.10267(2019).
[5] Case K M, Kac M[J]. J. Math. Phys., 14, 594(1973).
[6] Ablowitz M J, Ladik J F[J]. J. Math. Phys., 16, 598(1975).
[7] Ablowitz M J, Ladik J F[J]. J. Math. Phys., 17, 1011(1976).
[8] Ablowitz M J, Ladik J F[J]. Stud. Appl. Math., 55, 213(1976).
[9] Hirota R[J]. J. Phys. Soc. Jpn., 43, 1424(1977).
[10] Hirota R[J]. J. Phys. Soc. Jpn., 43, 2074(1977).
[11] Hirota R[J]. J. Phys. Soc. Jpn., 43, 2079(1977).
[12] Date E, Jimbo M, Miwa T[J]. J. Phys. Soc. Jpn., 51, 4116(1982).
[13] Date E, Jimbo M, Miwa T[J]. J. Phys. Soc. Jpn., 51, 4125(1982).
[14] Date E, Jimbo M, Miwa T[J]. J. Phys. Soc. Jpn., 52, 388(1983).
[15] Date E, Jimbo M, Miwa T[J]. J. Phys. Soc. Jpn., 52, 761(1983).
[16] Date E, Jimbo M, Miwa T[J]. J. Phys. Soc. Jpn., 52, 766(1983).
[17] Ueno K, [J]. Group Representations and Systems of Differential Equations Advanced Studies in Pure Mathematics, 4, 1-95(1984).
[18] Nijhoff F W, Quispel G R W, Capel H W[J]. Phys. Lett. A, 97, 125(1983).
[19] Nijhoff F W, Quispel G R W, Capel H W[J]. Phys. Lett. A, 98, 83(1983).
[20] Nijhoff F W, Capel H W, Wiersma G L, Quispel G R W[J]. Phys. Lett. A, 105, 267(1984).
[21] Nijhoff F W[J]. Lett. Math. Phys., 9, 235(1985).
[22] [J].
[23] Quispel G R W, Nijhoff F W, Capel H W, van ver Linden J[J]. Physica A, 125, 344(1984).
[24] Fokas A S, Ablowitz M[J]. Phys. Rev. Lett., 47, 1096(1981).
[25] Levi D, Benguria R[J]. Proc. Natl. Acad. Sci. U.S.A., 77, 5025(1980).
[26] Takahashi D, Satsuma J[J]. J. Phys. Soc. Jpn., 59, 3514(1990).
[27] Tokihiro T, Takahashi D, Matsukidaira J, Satsuma J[J]. Phys. Rev. Lett., 76, 3247(1996).
[28] Grammaticos B, Ramani A, Papageorgiou V G[J]. Phys. Rev. Lett., 67, 1825(1991).
[29] Ramani A, Grammaticos B, Hietarinta J[J]. Phys. Rev. Lett., 67, 1829(1991).
[30] Hietarinta J, Viallet C[J]. Phys. Rev. Lett., 81, 325(1998).
[31] Bellon M P, Viallet C[J]. Commun. Math. Phys., 204, 425(1999).
[32] Sakai H[J]. Commun. Math. Phys., 220, 165(2001).
[33] Bobenko A I, Suris Yu B[J]. Int. Math. Res. Not., 2002, 573(2002).
[34] Adler V E, Bobenko A I, Suris Yu B[J]. Commun. Math. Phys., 233, 513(2003).
[35] Nijhoff F W, Walker A J[J]. Glasg. Math. J., 43A, 109(2001).
[36] Nijhoff F W[J]. Phys. Lett. A, 297, 49(2002).
[37] Nijhoff F W, Atkinson J, Hietarinta J[J]. J. Phys. A: Math. Theor., 42, 404005(2009).
[38] Hietarinta J, Zhang D J[J]. J. Phys. A: Math. Theor., 42, 404006(2008).
[39] Atkinson J, Nijhoff F W[J]. Commun. Math. Phys., 299, 283(2010).
[40] Nijhoff F W, Atkinson J[J]. Int. Math. Res. Not., 2010, 3837(2010).
[41] Butler S, Joshi N[J]. Inverse Prob., 26, 115012(2010).
[42] Butler S[J]. Nonlinearity, 25, 1613(2012).
[43] Cao C W, Xu X X[J]. J. Phys. A: Math. Theor., 45, 055213(2012).
[44] Cao C W, Zhang G Y[J]. J. Phys. A: Math. Theor., 45, 095203(2012).
[45] Zhang D J, Zhao S L[J]. Stud. Appl. Math., 131, 72(2013).
[46] Bobenko A I, Its A[J]. Duke Math. J., 165, 2607(2016).
[47] Hietarinta J, Joshi N, Nijhoff F W[J](2016).
[48] Zhang D J, Chen S T[J]. Stud. Appl. Math., 125, 393(2010).
[49] Zhang D J, Chen S T[J]. Stud. Appl. Math., 125, 419(2010).
[50] Fu W, Qiao Z J, Sun J W, Zhang D J[J]. arXiv: 1307.3671(2013).
[51] Fu W, Qiao Z J, Sun J W, Zhang D J[J]. J. Nonlinear. Math. Phys., 22, 321(2015).
[52] Wahlquist H D, Estabrook F B[J]. Phys. Rev. Lett., 31, 1386(1973).
[53] Lamb JR G L[J]. Rev. Mod. Phys., 43, 99(1971).
[54] Chen H H[J]. Phys. Rev. Lett., 33, 925(1974).
[55] Orfanidis S J[J]. Phys. Rev. D, 18, 3828(1978).
[56] Bianchi L[J]. Rend. Lincei, 5, 2(1892).
[57] Bianchi L[J]. Lezioni di Geometria Differenziale 3rd Ed.(1894).
[58] Konopelchenko B G[J]. Phys. Lett. A, 87, 445(1982).
[59] Levi D[J]. J. Phys. A: Math. Gen., 14, 1083(1981).
[60] Adler V E, Yamilov R I[J]. J. Phys. A: Math. Gen., 27, 477(1994).
[61] Merola I, Ragnisco O, Tu G Z[J]. Inverse Prob., 10, 1315(1994).
[62] Zhang H W, Tu G Z, Oevel W, Fuchssteiner B[J]. J. Math. Phys., 32, 1908(1991).
[63] Chen K, Deng X, Zhang D J[J]. J. Nonlinear. Math. Phys., 24(Suppl.1), 18(2017).
[64] Cao C W, Zhang G Y[J]. Chin. Phys. Lett., 29, 050202(2012).
[65] Walker A J[J]. Ph.D. Thesis(2001).
[66] Adler V E[J]. Int. Math. Res. Not., 1998, 1(1998).
[67] Hietarinta J[J]. J. Nonlinear. Math. Phys., 12, 223(2005).
[68] Nijhoff F W, Papageorgiou V G, Capel H W, Quispel G R W[J]. Inverse Prob., 8, 597(1992).
[69] , Gel’fand I M eds[J]. Algebraic Aspects of Integrable Systems: In memory of Irene Dorfman, 237-260(1997).
[70] , Seiler R eds[J]. Discrete Integrable Geometry and Physics, 209-234(1999).
[71] Hietarinta J[J]. J. Phys. A: Math. Theor., 44, 165204(2011).
[72] Hietarinta J, Zhang D J[J]. preprint(2008).
[73] Atkinson J[J]. J. Phys. A: Math. Theor., 41, 135202(2008).
[74] Adler V E, Bobenko A I, Suris Yu B[J]. Funct. Anal. Appl., 43, 3(2009).
[75] Boll R[J]. J. Nonlinear. Math. Phys., 18, 337(2011).
[76] Boll R[J]. Ph.D Dissertation(2012).
[77] Adler V E, Bobenko A I, Suris Yu B[J]. Int. Math. Res. Not., 2012, 1822(2012).
[78] Miwa T[J]. Proc. Jpn. Acad., 58A, 9(1982).
[79] Konopelchenko B G, Schief W K[J]. Stud. Appl. Math., 109, 89(2002).
[80] Hirota R[J]. J. Phys. Soc. Jpn., 50, 3785(1981).
[81] Bianchi L[J]. Ann. Matem., 13, 177(1885).
[82] Atkinson J, Nieszporski M[J]. Int. Math. Res. Not., 2014, 4215(2014).
[83] Zhang D D, Zhang D J[J]. J. Nonlinear. Math. Phys., 25, 34(2018).
[84] Zhang D J, Cheng J W, Sun Y Y[J]. J. Phys. A: Math. Theor., 46, 265202(2013).
[85] Xenitidis P[J]. J. Phys. A: Math. Theor., 44, 435201(2011).
[86] Bridgman T, Hereman W, Quispel G R W, [J]. Found. Comput. Math., 13, 517(2013).
[87] Hietarinta J, Zhang D J[J]. J. Math. Phys., 51, 033505(2010).
[88] Hietarinta J, Zhang D J[J]. SIGMA, 7, 061(2011).
[89] Atkinson J, Hietarinta J, Nijhoff F W[J]. J. Phys. A: Math. Theor., 40, F1(2007).
[90] Konopelchenko B G, Schief W K[J]. J. Phys. A: Math. Gen., 35, 6125(2002).
