On the stability of periodic traveling waves for the modified Kawahara equation

DOI10.1080/00036811.2019.1659955zbMath1464.76043arXiv1904.01512OpenAlexW2970611850MaRDI QIDQ4989431

Fabrício Cristófani, Gisele Detomazi Almeida, Fábio M. Amorin Natali

Publication date: 25 May 2021

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.01512

zbMATH Keywords

linearizationorbital stabilitynonpositive spectrumFourier expansion method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hydrodynamic stability (76E99)

Cites Work

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• Lectures on the orbital stability of standing waves and application to the nonlinear Schrödinger equation
• Well-posedness issues on the periodic modified Kawahara equation
• Orbital stability of periodic traveling-wave solutions for the regularized Schamel equation
• Orbital stability of periodic traveling-wave solutions for the log-KdV equation
• Sufficient conditions for orbital stability of periodic traveling waves
• The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
• Positivity Properties of the Fourier Transform and the Stability of Periodic Travelling-Wave Solutions
• Positivity Properties and Stability of Solitary–Wave Solutions of Model Equations For Long Waves
• Fourier Series Coefficients for Powers of the Jacobian Elliptic Functions
• Orbital stability of periodic traveling wave solutions for the Kawahara equation
• The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations

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