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math.AP2026
Qualitative Aspects of Periodic Traveling Waves for the Sinh-Gordon equation
Beatriz Signori Lonardoni, Fabio Natali
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we est…
math.AP2025
On the orbital stability of periodic snoidal waves for the equation
B. S. Lonardoni, F. Natali
The main purpose of this paper is to investigate the global well-posedness and orbital stability of odd periodic traveling waves for the -equation in the Sobolev space of peri…
math.AP2025
Instability of the peaked traveling wave in a local model for shallow water waves
Fábio Natali, Dmitry E. Pelinovsky, Shuoyang Wang
The traveling wave with the peaked profile arises in the limit of the family of traveling waves with the smooth profiles. We study the linear and nonlinear stability of the peaked…