A New Exact Solution of Burgers' Equation with Linearized Solution. (30th August 2015)

• Record Type: Journal Article
• Authors: Kuo, Chun-Ku; Lee, Sen-Yung
• Other Names: Rodriguez-Lopez Rosana Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-08-30
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/414808
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper considers a general Burgers' equation with the nonlinear term coefficient being an arbitrary constant. Two identical solutions of the general Burgers' equation are separately derived by a direct integration method and the simplest equation method with the Bernoulli equation being the simplest equation. The proposed exact solutions overcome the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. In addition, a general Cole-Hopf transform is introduced. Finally, the proposed derived solution is compared with the perturbation solution and other existing exact solutions. A new phenomenon, which we named "kink sliding, " is observed.