dorsal/arxiv
View SchemaDynamics of kinks in the Ginzburg-Landau equation: Approach to a metastable shape and collapse of embedded pairs of kinks
| Authors | J. Rougemont |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9808007 |
| URL | https://arxiv.org/abs/patt-sol/9808007 |
| DOI | 10.1088/0951-7715/12/3/007 |
Abstract
We consider initial data for the real Ginzburg-Landau equation having two widely separated zeros. We require these initial conditions to be locally close to a stationary solution (the ``kink'' solution) except for a perturbation supported in a small interval between the two kinks. We show that such a perturbation vanishes on a time scale much shorter than the time scale for the motion of the kinks. The consequences of this bound, in the context of earlier studies of the dynamics of kinks in the Ginzburg-Landau equation, [ER], are as follows: we consider initial conditions $v_0$ whose restriction to a bounded interval $I$ have several zeros, not too regularly spaced, and other zeros of $v_0$ are very far from $I$. We show that all these zeros eventually disappear by colliding with each other. This relaxation process is very slow: it takes a time of order exponential of the length of $I$.
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"abstract": "We consider initial data for the real Ginzburg-Landau equation having two\nwidely separated zeros. We require these initial conditions to be locally close\nto a stationary solution (the ``kink\u0027\u0027 solution) except for a perturbation\nsupported in a small interval between the two kinks. We show that such a\nperturbation vanishes on a time scale much shorter than the time scale for the\nmotion of the kinks. The consequences of this bound, in the context of earlier\nstudies of the dynamics of kinks in the Ginzburg-Landau equation, [ER], are as\nfollows: we consider initial conditions $v_0$ whose restriction to a bounded\ninterval $I$ have several zeros, not too regularly spaced, and other zeros of\n$v_0$ are very far from $I$. We show that all these zeros eventually disappear\nby colliding with each other. This relaxation process is very slow: it takes a\ntime of order exponential of the length of $I$.",
"arxiv_id": "patt-sol/9808007",
"authors": [
"J. Rougemont"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1088/0951-7715/12/3/007",
"title": "Dynamics of kinks in the Ginzburg-Landau equation: Approach to a metastable shape and collapse of embedded pairs of kinks",
"url": "https://arxiv.org/abs/patt-sol/9808007"
},
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