1,284 research outputs found
Symmetries of nonlinear ordinary differential equations: the modified Emden equation as a case study
Lie symmetry analysis is one of the powerful tools to analyze nonlinear
ordinary differential equations. We review the effectiveness of this method in
terms of various symmetries. We present the method of deriving Lie point
symmetries, contact symmetries, hidden symmetries, nonlocal symmetries,
-symmetries, adjoint symmetries and telescopic vector fields of a
second-order ordinary differential equation. We also illustrate the algorithm
involved in each method by considering a nonlinear oscillator equation as an
example. The connections between (i) symmetries and integrating factors and
(ii) symmetries and integrals are also discussed and illustrated through the
same example. The interconnections between some of the above symmetries, that
is (i) Lie point symmetries and -symmetries and (ii) exponential
nonlocal symmetries and -symmetries are also discussed. The order
reduction procedure is invoked to derive the general solution of the
second-order equation.Comment: 31 pages, To appear in the proceedings of NMI workshop on nonlinear
integrable systems and their applications which was held at Centre for
Nonlinear Dynamics, Tiruchirappalli, Indi
Influence of field-like torque in synchronization of spin torque oscillators
The magnetization dynamics of two parallelly coupled spin torque oscillators,
destabilization of steady states and removal of multistability, are
investigated by taking into account the influence of field-like torque. It is
shown that the existence of such torque can cancel the effect of damping and
can, therefore, cause the oscillators to exhibit synchronized oscillations in
response to direct current. Further, our results show that the presence of
field-like torque enhances the power and Q-factor of the synchronized
oscillations. The validity of the above results is confirmed by numerical and
analytical studies based on the stochastic Landau-Lifshitz-Gilbert-Slonczewski
equation.Comment: 10 pages, 10 figures, Accepted for Publication in IEEE Transactions
on Magnetic
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