Results 11 to 20 of about 88 (42)

Solitary gravity-capillary water waves with point vortices [PDF]

Discrete Contin. Dyn. Syst. 36 (2016), no. 7, 3927-3959, 2015
We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting waves are also examined: We find that they depend significantly on the position of the point vortices in the water ...
arxiv   +1 more source

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model [PDF]

J. Differential Equations 262 (2017) 3235-3249, 2016
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity.
arxiv   +1 more source

Whitham equations and phase shifts for the Korteweg-deVries equation [PDF]

, 2020
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory is constructed to higher order. This allows the order one phase and the complete leading order solution to be obtained; the results are confirmed by extensive numerical ...
arxiv   +1 more source

Spectral stability of multiple periodic waves for the Schrodinger system with cubic nonlinearity [PDF]

arXiv, 2022
Results concerning the existence and spectral stability and instability of multiple periodic wave solutions for the nonlinear Schr\"odinger system with \textit{dnoidal} and \textit{cnoidal} profile will be determined in this manuscript. The spectral analysis for the corresponding linearized operator is established by using the comparison theorem and ...
arxiv  

Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation

Advances in Nonlinear Analysis
In this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect.
Moon Byungsoo, Yang Chao
doaj   +1 more source

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves [PDF]

J. Differential Equations 254 (2013), 1006-1096, 2011
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical ...
arxiv   +1 more source

On the nonlinear dynamics of the traveling-wave solutions of the Serre system [PDF]

Wave Motion (2017), Vol. 70, pp. 166-182, 2014
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes a high-order finite-element method with smooth, periodic splines in space and explicit Runge-Kutta methods in ...
arxiv   +1 more source

Instability and stability properties of traveling waves for the double dispersion equation [PDF]

Nonlinear Analysis, 133 (2016) 1-14, 2014
In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms $u_{xxxx}$
arxiv   +1 more source

A plethora of generalised solitary gravity-capillary water waves [PDF]

Journal of Fluid Mechanics (2015), Vol. 784, pp. 664-680, 2014
The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings).
arxiv   +1 more source

A variational reduction and the existence of a fully-localised solitary wave for the three-dimensional water-wave problem with weak surface tension [PDF]

Arch. Rational Mech. Anal. 228 (2018), 773-820, 2016
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a ...
arxiv   +1 more source