scholarly journals Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities

2021 ◽  
Vol 211 ◽  
pp. 112409
Author(s):  
Fei Justina Liu ◽  
Tai-Peng Tsai ◽  
Ian Zwiers
Keyword(s):  
Standing Waves ◽  
One Dimensional ◽  
Existence And Stability

scholarly journals Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth

2019 ◽  
Vol 23 (4) ◽  
Author(s):  
Kazuo Nishimura ◽  
Tadashi Shigoka
Keyword(s):  
Hopf Bifurcation ◽  
Endogenous Growth ◽  
Bifurcation Analysis ◽  
Stable Manifold ◽  
Closed Orbit ◽  
One Dimensional ◽  
Convex Structure ◽  
Equilibrium Dynamics ◽  
Closed Orbits ◽  
Existence And Stability

Abstract The present paper constructs a family of three-sector models of optimal endogenous growth, and conducts exact bifurcation analysis. In so doing, original six-dimensional equilibrium dynamics is decomposed into five-dimensional stationary autonomous dynamics and one-dimensional endogenously growing component. It is shown that the stationary dynamics thus decomposed undergoes supercritical Hopf bifurcation. It is inferred from the convex structure of our model that the dimension of a stable manifold of each closed orbit thus bifurcated in this five-dimensional dynamics should be two.

scholarly journals Real Space Imaging of One-Dimensional Standing Waves: Direct Evidence for a Luttinger Liquid

2004 ◽  
Vol 93 (16) ◽  
Author(s):  
Jhinhwan Lee ◽  
S. Eggert ◽  
H. Kim ◽  
S.-J. Kahng ◽  
H. Shinohara ◽  
...  
Keyword(s):  
Direct Evidence ◽  
Luttinger Liquid ◽  
Standing Waves ◽  
Real Space ◽  
One Dimensional

THE EFFECT OF TIME DELAY ON SPATIOTEMPORAL DYNAMICS IN ONE-DIMENSIONAL DISCRETE EXCITABLE MEDIA

2001 ◽  
Vol 15 (02) ◽  
pp. 167-176
Author(s):  
TAE-HOON CHUNG ◽  
SEUNGWHAN KIM
Keyword(s):  
Time Delay ◽  
Spatiotemporal Dynamics ◽  
Excitable Media ◽  
Winding Number ◽  
One Dimensional ◽  
Circle Maps ◽  
Pattern Complexity ◽  
Existence And Stability ◽  
Spatiotemporal Intermittency ◽  
The Stability

We investigate the effect of time delay on spatiotemporal dynamics in one-dimensional discrete excitable media with local delayed-interactions using coupled sine circle-maps. With the help of the stability analysis and numerical calculation of the pattern complexity entropy, we construct the phase diagram in the parameter space time delay and the nonlinear coupling. We find that the time delay affects the existence and stability of various regular states including homogeneously phase-locked and checkerboard states. In particular, the time delay induces the breakup of the homogeneously phase-locked state into spatiotemporal intermittency and the occurrence of multi-stability that depends on the winding number.

scholarly journals Standing Waves in One-Dimensional Resonator Containing an Ideal Isothermal Gas Affected by the Constant Mass Force

2017 ◽  
Vol 42 (2) ◽  
pp. 263-271
Author(s):  
Anna Perelomova
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Standing Waves ◽  
Ideal Gas ◽  
Excess Pressure ◽  
Mass Force ◽  
Constant Mass ◽  
Total Field ◽  
One Dimensional ◽  
Isothermal Gas

Abstract The study is devoted to standing acoustic waves in one-dimensional planar resonator which containing an ideal gas. A gas is affected by the constant mass force. Two types of physically justified boundary conditions are considered: zero velocity or zero excess pressure at both boundaries. The variety of nodal and antinodal points is determined. The conclusion is that the nodes of pressure and antinodes of velocity do not longer coincide, as well as antinodes of pressure and nodes of velocity. The entropy mode may contribute to the total field in a resonator. It is no longer isobaric, in contrast to the case when the external force is absent. Examples of perturbations inherent to the entropy mode in the volume of a resonator are discussed.

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