scholarly journals A group theoretical identification of integrable cases of the Liénard-type equation ẍ+f(x)ẋ+g(x)=0. I. Equations having nonmaximal number of Lie point symmetries

2009 ◽  
Vol 50 (8) ◽  
pp. 082702 ◽  
Author(s):  
S. N. Pandey ◽  
P. S. Bindu ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Type Equation ◽  
Lie Point Symmetries ◽  
Liénard Type Equation

scholarly journals Classification of Lie point symmetries for quadratic Liénard type equation ẍ+f(x)ẋ2+g(x)=0

2013 ◽  
Vol 54 (5) ◽  
pp. 053506 ◽  
Author(s):  
Ajey K. Tiwari ◽  
S. N. Pandey ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Type Equation ◽  
Lie Point Symmetries ◽  
Liénard Type Equation

Lie point symmetries classification of the mixed Liénard-type equation

2015 ◽  
Vol 82 (4) ◽  
pp. 1953-1968 ◽  
Author(s):  
Ajey K. Tiwari ◽  
S. N. Pandey ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Type Equation ◽  
Lie Point Symmetries ◽  
Liénard Type Equation

scholarly journals ON PERIODIC SOLUTIONS OF LIÉNARD TYPE EQUATIONS

2013 ◽  
Vol 18 (5) ◽  
pp. 708-716 ◽  
Author(s):  
Svetlana Atslega ◽  
Felix Sadyrbaev
Keyword(s):  
Periodic Solutions ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Type Equation ◽  
Convex Shape ◽  
Period Annulus ◽  
Conservative Equation ◽  
Liénard Type Equation

The Liénard type equation x'' + f(x, x')x' + g(x) = 0 (i) is considered. We claim that if the associated conservative equation x'' + g(x) = 0 has period annuli then a dissipation f(x, x') exists such that a limit cycle of equation (i) exists in a selected period annulus. Moreover, it is possible to define f(x, x') so that limit cycles appear in all period annuli. Examples are given. A particular example presents two limit cycles of non-convex shape in two disjoint period annuli.

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