Efficient computation of capillary-gravity generalized solitary waves [PDF]
, 2016 This paper is devoted to the computation of capillary-gravity solitary waves of the irrotational incompressible Euler equations with free surface. The numerical study is a continuation of a previous work in several points: an alternative formulation of ...
Clamond, Didier +2 more
core +12 more sources
Instability and stability properties of traveling waves for the double dispersion equation [PDF]
, 2002 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 $~p>1$, $~a\geq b>0$.
H.A. Erbay +21 more
core +6 more sources
Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise [PDF]
, 2008 We consider two exit problems for the Korteweg-de Vries equation perturbed by an additive white in time and colored in space noise of amplitude a. The initial datum gives rise to a soliton when a=0.
De Bouard, Anne, Gautier, Eric
core +8 more sources
On the Galilean invariance of some dispersive wave equations [PDF]
, 2013 Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of them is the Galilean symmetry, which
Abdulloev +67 more
core +6 more sources
Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations [PDF]
, 2013 After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties.
Abramowitz +19 more
core +6 more sources
Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling [PDF]
, 2016 We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons.
Carbone, Francesco +2 more
core +6 more sources
The non-local AFM water-wave method for cylindrical geometry [PDF]
, 2019 We develop an AFM (Ablowitz-Fokas-Musslimani) method applicable to studying water waves in a cylindrical geometry. As with the established AFM method for two-dimensional and three-dimensional water waves, the formulation involves only surface variables ...
Blyth, Mark, Parau, Emilian
core +1 more source
Numerical simulation of a solitonic gas in KdV and KdV-BBM equations [PDF]
, 2014 19 pages, 11 figures, 47 references. Other author's papers can be found at http://www.denys-dutykh.com/The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation.
Dutykh, Denys, Pelinovsky, Efim
core +5 more sources
Orbital stability of standing waves for supercritical NLS with potential on graphs
, 2018 In this paper we study the existence and stability of normalized standing waves for the nonlinear Schr\"odinger equation on a general starlike graph with potentials.
Ardila, Alex H.
core +1 more source
Application of the bifurcation method to the modified Boussinesq equation [PDF]
, 2014 In this paper, we investigate the modified Boussinesq equation $$u_{tt}- u_{xx}-\varepsilon u_{xxxx}-3(u^2)_{xx}+3(u^2u_x)_{x}=0.$$ Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t)$ is a solution, so is $1-u(x, t ...
Li, Shaoyong
core +2 more sources