LINEARIZED EULER'S VARIATIONAL EQUATIONS IN LAGRANGIAN COORDINATES

2008 ◽  
Author(s):  
GUY BOILLAT ◽  
YUE-JUN PENG
Keyword(s):  
Lagrangian Coordinates ◽  
Variational Equations

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.

The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

2016 ◽  
Vol 11 (2) ◽  
pp. 205-209
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Invariant Solution ◽  
Hydrodynamic Type ◽  
Lagrangian Coordinates ◽  
Hydrodynamic Equations ◽  
Rank 2 ◽  
Invariant Submodel ◽  
Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

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 Global existence of solutions for a multi-phase flow: A drop in a gas-tube

2016 ◽  
Vol 13 (02) ◽  
pp. 381-415
Author(s):  
Debora Amadori ◽  
Paolo Baiti ◽  
Andrea Corli ◽  
Edda Dal Santo
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Inviscid Fluid ◽  
Phase Flow ◽  
Lagrangian Coordinates ◽  
Large Initial Data ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Multi Phase Flow ◽  
Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

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