STABILITY OF HASIMOTO SOLITONS IN ENERGY SPACE FOR A FOURTH ORDER NONLINEAR SCHRODINGER TYPE EQUATION

Zhong Wang

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STABILITY OF HASIMOTO SOLITONS IN ENERGY SPACE FOR A FOURTH ORDER NONLINEAR SCHRODINGER TYPE EQUATION

机译：四阶非线性Schrodinger型方程能量空间中Hasimoto孤子的稳定性

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In this article we investigate the nonlinear stability of Hasimoto solitons, in energy space, for a fourth order Schrodinger equation (4NLS) which arises in the context of the vortex filament. The proof relies on a suitable Lyapunov functional, at the if H~2 level, which allows us to describe the dynamics of small perturbations. This stability result is also extended to Sobolev spaces H~m for all m ∈ Z_+ by employing the infinite conservation laws of 4NLS.

机译：在本文中，我们研究了在能量空间中Hasimoto孤子在能量空间中的非线性稳定性，该非线性稳定性是在涡旋丝的背景下出现的四阶Schrodinger方程（4NLS）。证明依赖于合适的Lyapunov函数（如果H〜2级别），这使我们能够描述小扰动的动力学。通过采用4NLS的无穷守恒律，将该稳定性结果扩展到所有m∈Z_ +的Sobolev空间H〜m。

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来源
《Discrete and continuous dynamical systems》 |2017年第7期|4091-4108|共18页
作者
Zhong Wang;
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作者单位

School of Mathematics and Big Data, Foshan University Foshan, Guangdong 528000, China;

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正文语种 eng
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关键词
Orbital stability; fourth order; Schrodinger equation; vortex filament;

机译：轨道稳定性;四阶薛定inger方程;涡旋丝;

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1. SOLITONS AND THEIR STABILITY IN HIGH DISPERSIVE SYSTEMS .1. FOURTH-ORDER NONLINEAR SCHRODINGER-TYPE EQUATIONS WITH POWER-LAW NONLINEARITIES [J] . Karpman VI., Shagalov AG. Physics Letters, A . 1997,第1a2期

机译：高色散系统中的孤子及其稳定性.1。具有幂律非线性的四阶非线性Schrodinger型方程
2. Optical solitons and stability analysis for the generalized fourth-order nonlinear Schrodinger equation [J] . Tang Xiao-Song, Li Biao Modern Physics Letters, B. Condensed Matter Physics, Statistical Physics, Applied Physics . 2019,第27期

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3. Stability of solitons described by nonlinear Schrodinger-type equations with higher-order dispersion [J] . Karpman VI., Shagalov AG. Physica, D. Nonlinear phenomena . 2000,第1a2期

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4. Modulational Instability of Bright Solitons of the Hyperbolic Nonlinear Schrodinger Equation [C] . S. P. Gorza, Emplit, M. Haelterman Conference on Lasers and Electro-Optics Europe . 2009

机译：双曲线非线性Schrodinger方程明亮孤子的调节不稳定性
5. Asymptotic dynamics of trapped solitons of nonlinear Schrodinger equations with potentials. [D] . Zhou, Gang. 2007

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STABILITY OF HASIMOTO SOLITONS IN ENERGY SPACE FOR A FOURTH ORDER NONLINEAR SCHRODINGER TYPE EQUATION

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