𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the nonlinear stability of plane waves for the ginzburg-landau equation

✍ Scribed by Todd Kapitula

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
406 KB
Volume
47
Category
Article
ISSN
0010-3640

No coin nor oath required. For personal study only.

✦ Synopsis

1 consider the nonlinear stability of plane wave solutions to a Ginzburg-Landau equation with additional fifth-order terms and cubic terms containing spatial derivatives. 1 show that, under the constraint that the diffusion coefficient be real, these waves are stable. Furthermore, it is shown that the radial component of the perturbation decays at a faster rate than the phase component of the perturbation as fcm. The result is also applicable to the classical Ginzburg-Landau equation. @

📜 SIMILAR VOLUMES

On the Validity of the degenerate Ginzbu
On the Validity of the degenerate Ginzburg—Landau equation
✍ A. Shepeleva 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB 👁 2 views

The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Gi

On the dynamical law of the Ginzburg-Lan
On the dynamical law of the Ginzburg-Landau vortices on the plane
✍ F.-H. Lin; J. X. Xin 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 164 KB 👁 2 views

We study the Ginzburg-Landau equation on the plane with initial data being the product of n well-separated +1 vortices and spatially decaying perturbations. If the separation distances are O(ε -1 ), ε 1, we prove that the n vortices do not move on the time scale the location of the j th vortex. The

Orbital Stability of Solitary Waves for
Orbital Stability of Solitary Waves for the Nonlinear Derivative Schrödinger Equation
✍ B.L. Guo; Y.P. Wu 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 445 KB

Consider herein are the stability of the solitary waves \(e^{-i \omega u s} e^{i \psi(x-t t)} a(x-v t)\) for the following nonlinear quintic derivative Schrödinger equation. \[ u_{t}=i u_{x x}+i\left(c_{3}|u|^{2}+c_{s}|u|^{4}\right) u+\left[\left(s_{0}+s_{2}|u|^{2}\right) u\right]_{v}, \quad u \in

On the Initial-Value Problem for the Gen
On the Initial-Value Problem for the Generalized Two-Dimensional Ginzburg–Landau Equation
✍ Hongjun Gao; Jinqiao Duan 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 198 KB

The Ginzburg᎐Landau-type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. Most work so far concentrates on Ginzburg᎐Landau-type equations Ž . with one spatial dimension 1D . In this paper, the author