Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:339

Article

Bluman, George¹  Cheviakov, Alexei E.¹  Senthilvelan, M.² 

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Bharathidasan Univ, Sch Phys, Ctr Nonlinear Dynam, Tiruchirappalli 620024, India

关键词: nonlinear oscillator;    blow-up behaviour;    Lane-Emden equation;    Lienard system;    symmetry;   

DOI  :  10.1016/j.jmaa.2007.06.076

来源: Elsevier

【 摘 要 】

In this paper, we consider a three-parameter class of Lienard type nonlinear dissipative systems of the form x + (b + 3kx)x + k(2)x(3) + bkx(2) + lambda x = 0. Since such dissipative systems admit an eight-parameter Lie group of point transformations, it follows that there exists a (complex) point transformation mapping such a system into the free particle system x = 0. Normally, such an explicit point transformation cannot be found. Here we find such an explicit point transformation through exploiting the group properties of the determining equations that lead to it. Consequently, we obtain the explicit general solution of such dissipative systems. Moreover, we completely characterize the asymptotic and/or finite time blow-up behaviour of such systems in terms of their three parameters and initial data. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free