Existence of Davey--Stewartson Type Solitary Waves for the Fully Dispersive Kadomtsev--Petviashvilii equation

DOI10.1137/21M1451518zbMath1497.76019arXiv2110.03971OpenAlexW3206543254MaRDI QIDQ5104096

Mats Ehrnström, D. V. Nilsson, Mark D. Groves

Publication date: 9 September 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.03971

zbMATH Keywords

convergencevariational methodelliptic-elliptic focusing Davey-Stewartson equationperturbed scaling

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Solitary waves for incompressible inviscid fluids (76B25) Soliton equations (35Q51)

Cites Work

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• Existence of solitary-wave solutions to nonlocal equations
• Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity
• The focusing singularity of the Davey-Stewartson equations for gravity- capillary surface waves
• Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation
• A variational reduction and the existence of a fully localised solitary wave for the three-dimensional water-wave problem with weak surface tension
• Solitary wave solutions to a class of modified Green-Naghdi systems
• On the variational principle
• Minimax theorems
• Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
• Dispersive estimates for full dispersion KP equations
• Solitary wave solutions of a Whitham-Boussinesq system
• Global bifurcation of solitary waves for the Whitham equation
• Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities
• Small amplitude traveling waves in the full-dispersion Whitham equation
• Remarks on the full dispersion Davey-Stewartson systems
• Solitary wave solutions to a class of Whitham-Boussinesq systems
• Remarks on the full dispersion Kadomtsev-Petviashvli equation
• Fully localised solitary-wave solutions of the three-dimensional gravity -- capillary water-wave problem
• A full dispersion asymptotic model to the water wave equations with surface tension
• On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
• On the existence of standing waves for a davey–stewartson system
• Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev–Petviashvili equation
• Generalized solitary waves in the gravity‐capillary Whitham equation
• Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity

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