arXiv subjects

Sabrina Amaral

Publications and source records attributed to Sabrina Amaral.

2 recordsLinked to original sources

arXiv2021

On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations

In this paper, we determine spectral stability results of periodic waves for the critical Korteweg-de Vries and Gardner equations. For the first equation, we show that both positive and zero mean periodic traveling wave solutions possess a threshold value which may provides us a rupture in the spectral stability. Concerning the second equation, we establish the existence of periodic waves using a Galilean transformation on the periodic cnoidal solution for the modified Korteweg-de Vries equation and for both equations, the threshold values are the same. The main advantage presented in our paper concerns in solving some auxiliary initial value problems to obtain the spectral stability.

math.AP↗

arXiv2021

On the existence, uniqueness and stability of Periodic Waves for the fractional Benjamin-Bona-Mahony equation

The existence, uniqueness and stability of periodic traveling waves for the fractional Benjamin-Bona-Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin-Bona-Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented.

math.AP↗