# Low-dimensional modelling of a generalised Burgers equation

Article

*Global Journal of Pure and Applied Mathematics.*3 (3), pp. 203-218.

Article Title | Low-dimensional modelling of a generalised Burgers equation |
---|---|

ERA Journal ID | 32290 |

Article Category | Article |

Authors | Li, Zhenquan (Author) and Roberts, A. J. (Author) |

Journal Title | Global Journal of Pure and Applied Mathematics |

Journal Citation | 3 (3), pp. 203-218 |

Number of Pages | 16 |

Year | 2007 |

Place of Publication | New Delhi, India |

ISSN | 0973-1768 |

0973-9750 | |

Web Address (URL) | http://www.ripublication.com/gjpam.htm |

Abstract | Burgers equation is one of the simplest nonlinear partial differential equations—it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a time-dependent function. Using a Wayne's transformation and centre manifold theory, we derive 1-mode and 2-mode centre manifold models of the generalized Burgers equations for bounded smooth time dependent coefficients. These modelings give some interesting extensions to existing results such as the similarity solutions using the similarity method. |

Keywords | differential equations; nonlinear models (statistics); binomial coefficients; diffusion |

ANZSRC Field of Research 2020 | 490510. Stochastic analysis and modelling |

510799. Particle and high energy physics not elsewhere classified | |

490407. Mathematical logic, set theory, lattices and universal algebra | |

490410. Partial differential equations | |

Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |

Byline Affiliations | University of the South Pacific, Fiji |

Department of Mathematics and Computing |

https://research.usq.edu.au/item/9zv5v/low-dimensional-modelling-of-a-generalised-burgers-equation

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