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Characteristic features of the dynamics of the Ginzburg-Landau equation in a plane domain

โœ Scribed by A. Yu. Kolesov; N. Kh. Rosov

Book ID
110553375
Publisher
SP MAIK Nauka/Interperiodica
Year
2000
Tongue
English
Weight
717 KB
Volume
125
Category
Article
ISSN
0040-5779

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โœ C. Bu ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 685 KB

We study the following Ginzburg-Landau equation (GL): \(u_{t}=(v+i x) u_{x x}-\) \((\kappa+i \beta)|u|^{2} u+\gamma u, v>0, \kappa>0, \alpha \neq 0\). For a full-line problem with \(u(x, 0)=\) \(u_{0}(x) \in H^{2}(-\infty, x)\), global existence-uniqueness is established. For a half-line problem wit

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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 t