-dimensional Auto-Bäcklund transformation and exact solutions to -dimensional Burgers system

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• 作者：Mingliang Wang^a ; ^b ; Jinliang Zhang^a ; ^{zhangjin6602@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xiangzheng Li^a
• 关键词：nn-dimensional Burgers system ; nn-dimensional BT ; nn-dimensional Cole&ndash ; Hopf transformation ; nn-dimensional Auto-BT ; SHB ; Exact solution
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：46-52
• 全文大小：1034 K

文摘

N$N$-dimensional Bäcklund transformation (BT), Cole–Hopf transformation and Auto-Bäcklund transformation (Auto-BT) of n$n$-dimensional Burgers system are derived by using simplified homogeneous balance (SHB). By the Auto-BT, another solution of the n$n$-dimensional Burgers system can be obtained provided that a particular solution of the Burgers system is given. Since the particular solution of n$n$-dimensional Burgers system can be given easily by the Cole–Hopf transformation, then using the Auto-BT repeatedly, more solutions of n$n$-dimensional Burgers system can be obtained successively.