Spectral properties of the Frechet derivatives of stratified steady Stokes waves

2025/12/03 by V. A. Kozlov, Kozlov, Vladimir
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #35Q31 #76N30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2512.03831

openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28

Abstract

We consider stratified steady water waves in a two dimensional channel. Our main subject is spectral properties of the Frechet derivatives of steady water Stokes waves. One of main results is the absence of subharmonic water waves in a neighborhood of a Stokes wave. The main assumption is formulated in terms of the eigenvalues of the Frechet derivative evaluated at this wave and considered in the class of periodic solutions of the same period. The first eigenvalue is always negative. We show that if the second eigenvalue is positive then there are no waves with multiple periods in a neighborhood of the Stokes wave.

Citations

• On the first bifurcation of solitary waves
• On first subharmonic bifurcations in a branch of Stokes waves
• The subharmonic bifurcation of Stokes waves on vorticity flow
• A sharp version of the Benjamin and Lighthill conjecture for steady waves with vorticity
• On the Benjamin--Lighthill conjecture for water waves with vorticity
• Global bifurcation of steady gravity water waves with critical layers
• Stratified Steady Periodic Water Waves

Cited by

• On the exchange of stability for the subcritical laminar flow

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• On the exchange of stability for the subcritical laminar flow
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• Steady waves in flows over periodic bottoms
• Transverse Instability of Stokes Waves at Finite Depth