Orbital stability of periodic traveling wave solutions for the Kawahara equation
Orbital stability of periodic traveling wave solutions for the Kawahara equation
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Kawahara 方程周期行波解的轨道稳定性
DOI：
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发表时间：
2017
期刊：
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通讯作者：
F. Natali
中科院分区：
文献类型：
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作者：
T. P. Andrade;Fabrício Cristófani;F. Natali
本文研究了Kawahara方程周期行波解的轨道稳定性。我们证明了周期性行波，在一定条件下，最小化一个方便的功能，通过使用Grillakis等人开发的方法的适应。Anal. 74，160-197（1987）]。确保轨道稳定性所需的光谱特性通过了解由Angulo和Natali建立的相关周期波的傅里叶变换的正性来获得[SIAM J. Math. Anal. 40，1123-1151（2008）]。
In this paper, we investigate the orbital stability of periodic traveling waves for the Kawahara equation. We prove that the periodic traveling wave, under certain conditions, minimizes a convenient functional by using an adaptation of the method developed by Grillakis et al. [J. Funct. Anal. 74, 160–197 (1987)]. The required spectral properties to ensure the orbital stability are obtained by knowing the positiveness of the Fourier transform of the associated periodic wave established by Angulo and Natali [SIAM J. Math. Anal. 40, 1123–1151 (2008)].