On a global Lagrangian construction for ordinary variational equations on 2-manifolds

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

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Existence and Properties of the Solutions via Fibering Method of a Class of Variational Equations with Non-Coercive Main Part with Some Applications

International Review of Aerospace Engineering (IREASE) ◽

10.15866/irease.v12i6.18584 ◽

2019 ◽

Vol 12 (6) ◽

pp. 302

Author(s):

Luisa Toscano

Keyword(s):

Main Part ◽

Variational Equations ◽

Fibering Method

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Second Existence Theorem for a Class of Variational Equations with Non-Coercive Main Part

International Review on Modelling and Simulations (IREMOS) ◽

10.15866/iremos.v12i5.18515 ◽

2019 ◽

Vol 12 (5) ◽

pp. 335

Author(s):

Luisa Toscano

Keyword(s):

Existence Theorem ◽

Main Part ◽

Variational Equations

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Numerical Method of Integrating the Variational Equations for Cauchy Problem Based on Differential Transformations

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v47.i9.60 ◽

2015 ◽

Vol 47 (9) ◽

pp. 63-75 ◽

Cited By ~ 1

Author(s):

Mikhail Yu. Rakushev

Keyword(s):

Cauchy Problem ◽

Numerical Method ◽

Variational Equations

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ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863508004226 ◽

2008 ◽

Vol 17 (03) ◽

pp. 285-297 ◽

Cited By ~ 1

Author(s):

ABDOSLLAM M. ABOBAKER ◽

A. B. MOUBISSI ◽

TH. B. EKOGO ◽

K. NAKKEERAN

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Pulse Width ◽

Schrodinger Equation ◽

Pulse Propagation ◽

Nonlinear Schrodinger Equation ◽

Fiber System ◽

Variational Equations ◽

Nonlinear Schrödinger ◽

The Given

We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

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