A New Exact Solution of Burgers' Equation with Linearized Solution

Chun Ku Kuo, Sen-Yung Lee

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Article number414808
JournalMathematical Problems in Engineering
Volume2015
DOIs
Publication statusPublished - 2015 Jan 1

Fingerprint

Burgers Equation
Exact Solution
Perturbation Solution
Kink
Coefficient
Term
Bernoulli
Linearity
Discontinuity
Transform
Zero
Arbitrary

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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A New Exact Solution of Burgers' Equation with Linearized Solution. / Kuo, Chun Ku; Lee, Sen-Yung.

In: Mathematical Problems in Engineering, Vol. 2015, 414808, 01.01.2015.

Research output: Contribution to journalArticle

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N2 - 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.

AB - 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.

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