We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund tr...We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund transformation.We apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete analogues.In the continuum limit,these differential-difference systems converge to their corresponding smooth equations.For these new integrable systems,their B¨acklund transformations and Lax pairs are derived.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11331008 and 11201425)the Hong Kong Baptist University Faculty Research(Grant No.FRG2/11-12/065)the Hong Kong Research Grant Council(Grant No.GRF HKBU202512)
文摘We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund transformation.We apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete analogues.In the continuum limit,these differential-difference systems converge to their corresponding smooth equations.For these new integrable systems,their B¨acklund transformations and Lax pairs are derived.
