Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms

DOI10.1016/0165-2125(89)90012-7zbMath0672.76022OpenAlexW2006789407MaRDI QIDQ1120392

Maarten W. Dingemans, Philip L.-F. Liu

Publication date: 1989

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0165-2125(89)90012-7

zbMATH Keywords

evolution equationsuneven bottombottom topographymodulated wave groupsmultiple-scale perturbation methodsnonlinear parabolic wave equationquasi-steady state problems

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30)

Related Items (5)

Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave ⋮ Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. II: nonlinear waves ⋮ A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom ⋮ A note on the third-order evolution equation of P. L.-F. Liu and M. W. Dingemans: ``Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms. ⋮ Nonelliptic Schrödinger equations

Cites Work

• Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth
• Derivation of the nonlinear Schrödinger equation for shoaling wave- groups
• On the development of packets of surface gravity waves moving over an uneven bottom
• Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study
• Refraction-diffraction model for weakly nonlinear water waves
• Oblique envelope solutions of the Davey–Stewartson equations in intermediate water depth
• Long waves induced by short-wave groups over an uneven bottom
• A parabolic equation for the combined refraction–diffraction of Stokes waves by mildly varying topography
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Nonlinear excitation of long-trapped waves by a group of short swells
• Stability of a plane soliton to infinitesimal two-dimensional perturbations
• Exact solutions of a three-dimensional nonlinear Schrödinger equation applied to gravity waves
• On three-dimensional packets of surface waves
• A general approach to linear and non-linear dispersive waves using a Lagrangian
• On slowly-varying Stokes waves
• The non-linear evolution of Stokes waves in deep water

This page was built for publication: Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms