Results 11 to 20 of about 160 (62)

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

, 2016
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.
Ablowitz, Barthélémy, Benjamin, Bona, Bona, Brenier, Carter, Choi, Clamond, Craig, Deconinck, Denys Dutykh, Dimitrios Mitsotakis, Duran, Dutykh, Dutykh, Dutykh, Dyachenko, El, Fenton, Green, Hairer, Hoefer, John Carter, Lavrentiev, Lax, Li, Marchant, Mirie, Mitsotakis, Ovsyannikov, Petviashvili, Ruban, Serre, Su, Su   +35 more
core   +12 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

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, S. Erbay, A. Erkip, Babaoglu, Bona, Boussinesq, Erbay, Erbay, Esfahani, Grillakis, Kutev, Le Coz, Levine, Liu, Liu, Ostrovskii, Porubov, Samsonov, Souganidis, Stubbe, Wang, Yacheng   +21 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, Dutykh, Denys, El, Gennady   +2 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, Antnonopoulos, Barth, Barth, DENYS DUTYKH, DIDIER CLAMOND, DIMITRIOS MITSOTAKIS, Dougalis, Ghidaglia, Isaacson, Kolgan, Lamb, Mei, PAUL MILEWSKI, Petrov, Seabra-Santos, Stoker, van Leer, Zheleznyak, Zheleznyak   +19 more
core   +7 more sources

A boussinesq-type model for waves generated by flow over a bump

, 2014
A uniform ow disturbed by a bump is studied. The eect of the disturbance is presented at the surface, generating wave. The wave propagation is modeled into a couple of equations, in terms of the surface elevation and the depth average velocity.
L. Wiryanto, S. Mungkasi
semanticscholar   +1 more source

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, Antonopoulos, Barthélémy, Benjamin, Benjamin, Bona, Bona, Bona, Bona, Bona, Boussinesq, Broer, Camassa, Carter, Chen, Chhay, Chhay, Christov, Clamond, Courtenay Lewis, Craig, Craik, de Saint-Venant, Degasperis, Dougalis, Dougalis, Dullin, Dutykh, Dutykh, Dutykh, Fenton, Fetecau, Gardner, Green, Green, Grimshaw, Johnson, Johnson, Kim, Kim, Korteweg, Lakoba, Lannes, Lax, Li, Li, Li, Longuet-Higgins, Luke, Miura, Nwogu, Olver, Pava, Pego, Pelinovsky, Peregrine, Peregrine, Petrov, Petviashvili, Salmon, Serre, Stoker, Su, Tanaka, Whitham, Yang, Zabusky, Zakharov   +67 more
core   +6 more sources

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

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

Diverse soliton wave profile assessment to the fractional order nonlinear Landau-Ginzburg-Higgs and coupled Boussinesq-Burger equations

Results in Physics
The space–time fractional Landau-Ginzburg-Higgs equation and coupled Boussinesq-Burger equation describe the behavior of nonlinear waves in the tropical and mid-latitude troposphere, exhibiting weak scattering, extended connections, arising from the ...
Anamika Podder, Mohammad Asif Arefin, Khaled A. Gepreel, M. Hafiz Uddin, M. Ali Akbar   +4 more
doaj   +1 more source