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

doi:10.1007/s10473-020-0402-4

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (4): 910-920.doi: 10.1007/s10473-020-0402-4

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

Zongguang LI, Rui LIU

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).

Abstract

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

CLC Number:

34A20

Zongguang LI, Rui LIU. BLOW-UP SOLUTIONS FOR A CASE OF b-FAMILY EQUATIONS[J].Acta mathematica scientia,Series B, 2020, 40(4): 910-920.

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

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