数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 910-920.doi: 10.1007/s10473-020-0402-4

• 论文 • 上一篇    下一篇

BLOW-UP SOLUTIONS FOR A CASE OF b-FAMILY EQUATIONS

李宗广, 刘锐   

  1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2019-06-24 修回日期:2019-12-28 出版日期:2020-08-25 发布日期:2020-08-21
  • 通讯作者: Rui LIU E-mail:scliurui@scut.edu.cn
  • 作者简介:Zongguang LI,E-mail:337303753@qq.com
  • 基金资助:
    This research was partially supported by the National Natural Science Foundation of China (11771152, 11971176), Guangdong Basic and Applied Basic Research Foundation (2019B151502062), and the Fundamental Research Founds for the Central Universities (2019MS111).

BLOW-UP SOLUTIONS FOR A CASE OF b-FAMILY EQUATIONS

Zongguang LI, Rui LIU   

  1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2019-06-24 Revised:2019-12-28 Online:2020-08-25 Published:2020-08-21
  • Contact: Rui LIU E-mail:scliurui@scut.edu.cn
  • Supported by:
    This research was partially supported by the National Natural Science Foundation of China (11771152, 11971176), Guangdong Basic and Applied Basic Research Foundation (2019B151502062), and the Fundamental Research Founds for the Central Universities (2019MS111).

摘要: In this article, we study the blow-up solutions for a case of b-family equations. Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution. Not only are the expressions of these blow-up solutions given, but also their relationships are discovered. In particular, it is found that two bounded solitary solutions are bifurcated from an elliptic blow-up solution.

关键词: b-family equation, blow-up solutions, qualitative theory, bifurcation method

Abstract: In this article, we study the blow-up solutions for a case of b-family equations. Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution. Not only are the expressions of these blow-up solutions given, but also their relationships are discovered. In particular, it is found that two bounded solitary solutions are bifurcated from an elliptic blow-up solution.

Key words: b-family equation, blow-up solutions, qualitative theory, bifurcation method

中图分类号: 

  • 34A20