Self-similar planar curves related to modified Korteweg-de Vries equation

被引：12

作者：

Perelman, G.

Vega, L. ^{[1
]}

机构：

[1] Univ Basque Country, E-48080 Bilbao, Spain

[2] Ecole Polytech, F-75230 Paris, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 235卷 / 01期

关键词：

planar curves; selfsimilarity; modified Korteweg-de Vries equation; LOCALIZED INDUCTION APPROXIMATION; SOLITONS; DYNAMICS;

D O I：

10.1016/j.jde.2006.12.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We exhibit a time reversible geometric flow of planar curves which can develop singularities in finite time within the uniform topology. The example is based on the construction of selfsimilar solutions of modified Korteweg-de Vries equation of a given (small) mean. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：56 / 73

页数：18

共 13 条

[1] Ablowitz MJ, 1981, Solitons and the Inverse Scattering Transform
[2] [Anonymous], LECT NOTES MATH
[3] CHEMIN JY, 1994, ANN SCI ECOLE NORM S, V265, P517
[4] Da Rios LS., 1906, REND CIRC MAT PALERM, V22, P117, DOI DOI 10.1007/BF03018608
[5] DELAHOZ F, COMMUNICATION
[6] SOLITONS, EULER EQUATION, AND VORTEX PATCH DYNAMICS
GOLDSTEIN, RE
PETRICH, DM
[J]. PHYSICAL REVIEW LETTERS, 1992, 69 (04) : 555 - 558
[7] Self-similar solutions of the localized induction approximation: singularity formation
Gutierrez, S
Vega, L
[J]. NONLINEARITY, 2004, 17 (06) : 2091 - 2136
[8] Formation of singularities and self-similar vortex motion under the localized induction approximation
Gutiérrez, S
Rivas, J
Vega, L
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (5-6) : 927 - 968
[9] SOLITON ON A VORTEX FILAMENT
HASIMOTO, H
[J]. JOURNAL OF FLUID MECHANICS, 1972, 51 (FEB8) : 477 - &
[10] On the ill-posedness of some canonical dispersive equations
Kenig, CE
Ponce, G
Vega, L
[J]. DUKE MATHEMATICAL JOURNAL, 2001, 106 (03) : 617 - 633

← 1 2 →