N-dimensional Auto-B\"acklund Transformation and Exact Solutions to n-dimensional Burgers System
Mingliang Wang, Jinliang Zhang, and Xiangzheng Li
TL;DR
This paper derives n-dimensional Bäcklund and Cole-Hopf transformations for the Burgers system, enabling the generation of multiple solutions through Auto-Bäcklund transformations based on a known particular solution.
Contribution
It introduces a method to obtain Auto-Bäcklund transformations for the n-dimensional Burgers system using simplified homogeneous balance, expanding solution-generation techniques.
Findings
Derived n-dimensional Bäcklund and Cole-Hopf transformations.
Established a recursive method to generate multiple solutions.
Demonstrated the effectiveness of Auto-Bäcklund transformations in solving the Burgers system.
Abstract
N-dimensional B\"acklund transformation (BT), Cole-Hopf transformation and Auto-B\"acklund transformation (Auto-BT) of n-dimensional Burgers system are derived by using simplified homogeneous balance (SHB). By the Auto-BT, another solution of the n-dimensional Burgers system can be obtained provided that a particular solution of the Burgers system is given. Since the particular solution of n-dimensional Burgers system can be given easily by the Cole-Hopf transformation, then using the Auto-BT repeatedly, more solutions of n-dimensional Burgers system can be obtained successively
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Numerical methods for differential equations