Stationary solutions for the one-dimensional Nordström–Vlasov system

2009 ◽  
Vol 64 (3–4) ◽  
pp. 155-183
Author(s):  
Mihai Bostan
Keyword(s):  
Stationary Solutions ◽  
One Dimensional ◽  
The One

Counting stationary solutions of the Cahn–Hilliard equation by transversality arguments

1995 ◽  
Vol 125 (2) ◽  
pp. 351-370 ◽  
Author(s):  
M. Grinfeld ◽  
A. Novick-Cohen
Keyword(s):  
Stationary Solutions ◽  
Cubic Nonlinearity ◽  
One Dimensional ◽  
Level Curves ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation ◽  
The One

In this paper we use arguments based on Picard-Fuchs equations and transversality of intersections of level curves to obtain an exact count of the number of stationary solutions of the one-dimensional Cahn-Hilliard equation with a cubic nonlinearity.

scholarly journals INVESTIGATION OF STATIONARY SOLUTIONS OF VISCOELASTIC MELT SPINNING EQUATIONS AND STABILITY WITH RESPECT TO INCREASING VISCOELASTICITY

2010 ◽  
Vol 15 (3) ◽  
pp. 287-298 ◽  
Author(s):  
R. Dhadwal ◽  
S. K. Kudtarkar
Keyword(s):  
Constitutive Equation ◽  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Melt Spinning ◽  
Stationary Solutions ◽  
Model Parameter ◽  
One Dimensional ◽  
Spinning Process ◽  
The Stability ◽  
The One

The one‐dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take‐up velocity was found. Further, the value of the Giesekus model parameter for which the fibre exhibits Newtonian behaviour was found analytically. Using numerical simulations it was shown that below this value of the parameter the fluid shows extension thickening behaviour and above, extension thinning. In this context, by simulating the non‐stationary equations the effect of viscoelasticity on the stability of the spinning process was studied.

scholarly journals Study of Attractive Nonlinearity by 1-D Nonlinear Schrödinger Equation in the Bose–Einstein Condensate

1970 ◽  
Vol 33 (1) ◽  
pp. 87-98
Author(s):  
ML Rahman ◽  
Y Haque ◽  
SK Das ◽  
MM Hossain ◽  
MH Rashid
Keyword(s):  
Boundary Condition ◽  
Small Perturbation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
One Dimensional ◽  
Bright Solitons ◽  
Non Linear ◽  
The One ◽  
Bose Einstein ◽  
Academy Of Sciences

The work represents and investigates the stationary solutions of the one-dimensional Non-linear Schrödinger Equation (NLSE), for attractive non-linearity, in the Bose-Einstein condensates (BEC) under the box boundary condition and calculates the characteristics of internal modes of bright solitons (eigen modes of small perturbation of the condensate). DOI: 10.3329/jbas.v33i1.2953 Journal of Bangladesh Academy of Sciences, Vol. 33, No. 1, 87-98, 2009

Stationary solutions to a nonlinear Schrödinger equation with potential in one dimension

2003 ◽  
Vol 133 (2) ◽  
pp. 409-437 ◽  
Author(s):  
Mihai Mariş
Keyword(s):  
Schrödinger Equation ◽  
Sound Velocity ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Nonlinear Schrodinger Equation ◽  
One Dimension ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
The One

We study the one-dimensional Gross-Pitaevskii-Schrödinger equation with a potential U moving at velocity v. For a fixed v less than the sound velocity, it is proved that there exist two time-independent solutions if the potential is not too big.

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