中国物理B ›› 2001, Vol. 10 ›› Issue (12): 1091-1095.doi: 10.1088/1009-1963/10/12/301

• GENERAL •    下一篇

THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS

白成林   

  1. Department of Communication Engineering, Liaocheng Teachers' College, Liaocheng 252059, China
  • 收稿日期:2001-03-01 修回日期:2001-07-17 出版日期:2005-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 69577009) and Natural Science Foundation of Shandong Province, China (Grant No. Q99G11).

THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS

Bai Cheng-lin (白成林)   

  1. Department of Communication Engineering, Liaocheng Teachers' College, Liaocheng 252059, China
  • Received:2001-03-01 Revised:2001-07-17 Online:2005-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 69577009) and Natural Science Foundation of Shandong Province, China (Grant No. Q99G11).

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摘要： Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.

Abstract: Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.

Key words: (2+1)-dimensional Burgers equation, higher-order Burgers equation, extended homogeneous balance method, exact solutions

中图分类号:  (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

  • 03.75.Lm
02.30.Sa (Functional analysis) 02.30.Hq (Ordinary differential equations)