On the stability of weakly nonlinear short waves on finite-amplitude long gravity waves

DOI10.1017/S0022112092002635zbMath0757.76007OpenAlexW2121694258MaRDI QIDQ4021178

Jun Zhang, W. K. Melville

Publication date: 17 January 1993

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0022112092002635

zbMATH Keywords

modulated nonlinear Schrödinger equationsteady envelope solutions

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Hydrodynamic stability (76E99)

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Cites Work

• On the dynamics of unsteady gravity waves of finite amplitude Part 2. Local properties of a random wave field
• On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory
• On a fourth-order envelope equation for deep-water waves
• The energy and action of small waves riding on large waves
• The dispersion of short wavelets in the presence of a dominant long wave
• The propagation of short surface waves on longer gravity waves
• The disintegration of wave trains on deep water Part 1. Theory