107 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre National de la Recherche ScientifiqueFR169 papers
- Université Savoie Mont BlancFR162 papers
- Laboratoire d’Analyse et de Mathématiques AppliquéesFR85 papers
- Institut National des Sciences Mathématiques et de leurs InteractionsFR69 papers
- Laboratoire de Mathématiques Blaise PascalFR33 papers
- Laboratoire Jean-Alexandre DieudonnéFR21 papers
- Laboratoire Optimisation de la Conception et Ingénierie de l'EnvironnementFR21 papers
- Université Grenoble AlpesFR19 papers
- Université Paris-Est CréteilFR19 papers
- University College DublinIE17 papers
- Université Nice Sophia AntipolisFR16 papers
- Pontifícia Universidade Católica do ParanáBR15 papers
40 papers · 1 filter
Effects of vorticity on the travelling waves of some shallow water two-component systems
Denys Dutykh, Delia Ionescu-Kruse
In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Name…
Long wave interaction with a partially immersed body. Part I: Mathematical models
Gayaz Khakimzyanov, Denys Dutykh
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general ma…
On time relaxed schemes and formulations for dispersive wave equations
Jean-Paul Chehab, Denys Dutykh
The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for…
Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth
Didier Clamond, Denys Dutykh
This paper describes an efficient algorithm for computing steady two-dimensional surface gravity wave in irrotational motion. The algorithm complexity is O(N log N), N being the nu…
On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime
Dimitrios Mitsotakis, Denys Dutykh, Aydar Assylbekuly +1
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possib…
Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves
Didier Clamond, Denys Dutykh
In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity lo…
Algebraic method for constructing singular steady solitary waves: A case study
Didier Clamond, Denys Dutykh, André Galligo
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady…
Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics
Didier Clamond, Denys Dutykh, Dimitrios Mitsotakis
For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to im…
Coupling Conditions for Water Waves at Forks
Jean-Guy Caputo, Denys Dutykh, Bernard Gleyse
We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using…
Resonance enhancement by suitably chosen frequency detuning
Denys Dutykh, Elena Tobisch
In this Letter we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation…
Evolution of Random Wave Fields in the Water of Finite Depth
Denys Dutykh
The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict…
Numerical study of the generalised Klein-Gordon equations
Denys Dutykh, Marx Chhay, Didier Clamond
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational form…
Some special solutions to the Hyperbolic NLS equation
Laurent Vuillon, Denys Dutykh, Francesco Fedele
The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili…
On the Galerkin / finite-element method for the Serre equations
Dimitrios Mitsotakis, Boaz Ilan, Denys Dutykh
A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-…
Extreme wave runup on a vertical cliff
Francesco Carbone, Denys Dutykh, John M. Dudley +1
Wave impact and run-up onto vertical obstacles are among the most important phenomena which must be taken into account in the design of coastal structures. From linear wave theory,…
Run-up amplification of transient long waves
Themistoklis Stefanakis, Shanshan Xu, Denys Dutykh +1
The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformati…
Generation of two-dimensional water waves by moving bottom disturbances
Hayk Nersisyan, Denys Dutykh, Enrique Zuazua
We investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater…
Geometric numerical schemes for the KdV equation
Denys Dutykh, Marx Chhay, Francesco Fedele
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous s…
Solitary wave interaction in a compact equation for deep-water gravity waves
Francesco Fedele, Denys Dutykh
In this study we compute numerical traveling wave solutions to a compact version of the Zakharov equation for unidirectional deep-water waves recently derived by Dyachenko & Zakhar…
Special solutions to a compact equation for deep-water gravity waves
Francesco Fedele, Denys Dutykh
Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential f…
Modified Shallow Water Equations for significantly varying seabeds
Denys Dutykh, Didier Clamond
In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom under…
Boussinesq modeling of surface waves due to underwater landslides
Denys Dutykh, Henrik Kalisch
Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the bar…
Hamiltonian form and solitary waves of the spatial Dysthe equations
Francesco Fedele, Denys Dutykh
The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are u…
Hamiltonian description and traveling waves of the spatial Dysthe equations
Francesco Fedele, Denys Dutykh
The spatial version of the fourth-order Dysthe equations describe the evolution of weakly nonlinear narrowband wave trains in deep waters. For unidirectional waves, the hidden Hami…