Spectral stability for classical periodic waves of the Ostrovsky and\n short pulse models

2016/04/11 by Sevdzhan Hakkaev, Hakkaev, Sevdzhan, Milena Stanislavova +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1604.03024

openalex publication_date 2016/04/11 · openalex created_date 2022/09/23 · openalex updated_date 2026/07/28

Abstract

We consider the Ostrovsky and short pulse models in a symmetric spatial\ninterval, subject to periodic boundary conditions. For the Ostrovsky case, we\nrevisit the classical periodic traveling waves and for the short pulse model,\nwe explicitly construct traveling waves in terms of Jacobi elliptic functions.\nFor both examples, we show spectral stability, for all values of the\nparameters. This is achieved by studying the non-standard eigenvalue problems\nin the form L u= la u', where L is a Hill operator.\n

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