Solitons of Discrete Curve Shortening
نویسندگان
چکیده
منابع مشابه
The Zoo of Solitons for Curve Shortening in R
We provide a detailed description of solutions of Curve Shortening in Rn that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic properties of their ends. We find generalized helices, and a connection with curve shortening on the unit sphere Sn−1. Expanding rotating solitons turn out to be ...
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In this paper, we analyze the results of triangles under discrete curve shortening flow, specifically isosceles triangles with top angles greater than π3 , and scalene triangles. By considering the location of the three vertices of the triangle after some small time , we use the definition of the derivative to calculate a system of differential equations involving parameters that can describe t...
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امروزه سالیتون ها بعنوان امواج جایگزیده ای که تحت شرایط خاص بدون تغییر شکل در محیط منتشر می-شوند، زمینه مطالعات گسترده ای در حوزه اپتیک غیرخطی هستند. در این راستا توجه به پدیده پراش گسسته، که بعنوان عامل پهن شدگی باریکه نوری در آرایه ای از موجبرهای جفت شده، ظاهر می گردد، ضروری است، زیرا سالیتون های گسسته از خنثی شدن پراش گسسته در این سیستم ها بوسیله عوامل غیرخطی بوجود می آیند. گسستگی سیستم عامل...
Curve Shortening and Grayson’s Theorem
In this chapter and the next we discuss the curve shortening flow (CSF). A number of important techniques in the field of geometric flows exhibit themselves in the curve shortening flow in an elegant and less technical way. The CSF was proposed in 1956 by Mullins to model the motion of idealized grain boundaries. In 1978 Brakke studied the mean curvature flow, of which the CSF is the 1-dimensio...
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We derive evolution equations describing light propagation in an array of coupled-waveguide resonators and predict the existence of discrete cavity solitons. We identify stable, unstable, and oscillating solitons by varying the coupling strength between the anticontinuous and the continuous limit.
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2016
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-016-0572-5