Nonlinear instability of a critical traveling wave in the generalized Korteweg-de Vries equation

Comech A; Cuccagna S; Pelinovsky DE

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Nonlinear instability of a critical traveling wave in the generalized Korteweg-de Vries equation

机译：广义Korteweg-de Vries方程中临界行波的非线性不稳定性

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摘要

We prove the instability of a "critical" solitary wave of the generalized Korteweg de Vries equation, the one with the speed at the border between the stability and instability regions. The instability mechanism involved is "purely nonlinear" in the sense that the linearization at a critical soliton does not have eigenvalues with positive real part. We prove that critical solitons correspond generally to the saddle-node bifurcation of two branches of solitons.

机译：我们证明了广义Korteweg de Vries方程的“临界”孤波的不稳定性，该孤波的速度在稳定性和不稳定性区域之间。在临界孤子处的线性化不具有正实部的特征值的意义上，所涉及的不稳定机制是“纯粹的非线性”。我们证明临界孤子通常对应于孤子两个分支的鞍节点分叉。

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《SIAM Journal on Mathematical Analysis》 |2007年第1期|共33页
作者
Comech A; Cuccagna S; Pelinovsky DE;
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正文语种 eng
中图分类数学分析;
关键词
korteweg-de Vries equation; critical soliton; dynamic instability; orbital stability; BLOW-UP SOLUTIONS; SOLITARY WAVES; ASYMPTOTIC STABILITY; KDV EQUATION; EXISTENCE; SOLITONS; ENERGY; TIME;

机译：korteweg-de Vries方程临界孤子动态不稳定性轨道稳定性爆破解孤波渐近稳定性KDV方程存在;孤子能量时间;

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专利

1. Nonlinear instability of a critical traveling wave in the generalized Korteweg-de Vries equation [J] . Comech A, Cuccagna S, Pelinovsky DE SIAM Journal on Mathematical Analysis . 2007,第1期

机译：广义Korteweg-de Vries方程中临界行波的非线性不稳定性
2. Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrodinger equations [J] . Pava JA, Natali FMA Physica, D. Nonlinear phenomena . 2009,第6期

机译：临界Korteweg-de Vries和非线性Schrodinger方程的周期行波解的稳定性和不稳定性
3. NONLINEAR INSTABILITY OF A CRITICAL TRAVELING WAVE IN THE GENERALIZED KORTEWEG–DE VRIES EQUATION [J] . ANDREW COMECH, SCIPIO CUCCAGNA, DMITRY E. PELINOVSKY SIAM Journal on Mathematical Analysis . 2008,第1期

机译：广义Korteweg-De VRies方程中关键行波的非线性失稳。
4. Some mathematical aspects of the correspondence between the generalized nonlinear Schr?dinger equation and the generalized Korteweg-de Vries equation [C] . Renato Fedele, Sergio De Nicola, Dan Grecu, International Symposium on Cutting Edge Plasma Physics . 2009

机译：广义非线性SCHR？Dinger方程与广义Korteweg-de Vries方程的对应关系的一些数学方面
5. Some results on the one-dimensional linear wave equation with van der Pol type nonlinear boundary conditions and the Korteweg-de Vries-Burgers equation. [D] . Feng, Zhaosheng. 2004

机译：关于具有范德波尔型非线性边界条件的一维线性波动方程和Korteweg-de Vries-Burgers方程的一些结果。
6. Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations [O] . S M Rayhanul Islam, Kamruzzaman Khan, M Ali Akbar -1

机译：非定常Korteweg-de Vries和时间正则化长波方程的精确解
7. Nonlinear instability of a critical traveling wave in the generalized Korteweg – de Vries equation [O] . Andrew Comech, Scipio Cuccagna, Dmitry E. Pelinovsky 2008

机译：广义Korteweg-de Vries方程中临界行波的非线性不稳定性
8. Variable Coefficient Korteweg-de Vries Equations and Travelling Waves in an Inhomogeneous Medium [R] . Baby, B. V. 1987

机译：非均匀介质中变系数Korteweg-de Vries方程和行波

Nonlinear instability of a critical traveling wave in the generalized Korteweg-de Vries equation

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