Infinitesimal symmetry transformations. II. Some one‐dimensional nonlinear systems

1985 ◽  
Vol 26 (4) ◽  
pp. 593-600 ◽  
Author(s):  
M. Aguirre ◽  
J. Krause
Keyword(s):  
Nonlinear Systems ◽  
One Dimensional ◽  
Infinitesimal Symmetry ◽  
Symmetry Transformations

Optimal systems and their group-invariant solutions to geodesic equations

2019 ◽  
Vol 16 (09) ◽  
pp. 1950135
Author(s):  
Bismah Jamil ◽  
Tooba Feroze ◽  
Muhammad Safdar
Keyword(s):  
Nonlinear Systems ◽  
Separation Of Variables ◽  
Noether Symmetries ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Group Invariant ◽  
First Order ◽  
Geodesic Equations ◽  
Integrating Factor ◽  
Group Invariant Solutions

We find one-dimensional optimal systems of the Lie subalgebras of Noether symmetries associated with systems of geodesic equations. Further, we find invariants corresponding to each element of the derived optimal system. The derived invariants are shown to reduce systems of geodesic equations (nonlinear systems of quadratically semi-linear second-order ordinary differential equations (ODEs)) to nonlinear systems of first-order ODEs. The resulting systems are solved via known methods (e.g. separation of variables, integrating factor, etc.). In some cases, we provide exact solutions of these systems of geodesic equations.

Localization in One-dimensional Quasi-periodic Nonlinear Systems

2014 ◽  
Vol 24 (1) ◽  
pp. 116-158 ◽  
Author(s):  
Jiansheng Geng ◽  
Jiangong You ◽  
Zhiyan Zhao
Keyword(s):  
Nonlinear Systems ◽  
One Dimensional

One-dimensional waves in disperse nonlinear systems

1970 ◽  
Vol 13 (2) ◽  
pp. 121-161 ◽  
Author(s):  
A. V. Gaponov ◽  
L. A. Ostrovskii ◽  
M. I. Rabinovich
Keyword(s):  
Nonlinear Systems ◽  
One Dimensional
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