scholarly journals Higher regularity and uniqueness for inner variational equations

2021 ◽  
Vol 61 (1) ◽  
Author(s):  
Gaven Martin ◽  
Cong Yao
Keyword(s):  
Variational Equations ◽  
Higher Regularity

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

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.

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

2008 ◽  
Vol 17 (03) ◽  
pp. 285-297 ◽  
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.

Exponential Stability in Mean Square and Stochastic Variational Equations

2011 ◽  
Author(s):  
Adina Păucă ◽  
Diana Stoica ◽  
Ludovic Dan Lemle ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Mean Square ◽  
Variational Equations ◽  
Stability In Mean Square

scholarly journals Variational Equations of Schroedinger-Type in Non-cylindrical Domains

2001 ◽  
Vol 171 (1) ◽  
pp. 63-87 ◽  
Author(s):  
Marco Luigi Bernardi ◽  
Gianni Arrigo Pozzi ◽  
Giuseppe Savaré
Keyword(s):  
Variational Equations ◽  
Cylindrical Domains

scholarly journals Integrability of Hamiltonian systems and differential Galois groups of higher variational equations

2007 ◽  
Vol 40 (6) ◽  
pp. 845-884 ◽  
Author(s):  
J MORALESRUIZ ◽  
J RAMIS ◽  
C SIMO
Keyword(s):  
Hamiltonian Systems ◽  
Galois Groups ◽  
Variational Equations

Variational equations for structurally anisotropic plates

1973 ◽  
Vol 9 (5) ◽  
pp. 527-531
Author(s):  
L. V. Endzhievskii ◽  
N. P. Abovskii
Keyword(s):  
Variational Equations ◽  
Anisotropic Plates
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