Results 11 to 20 of about 125 (34)

Three‐dimensional Korteweg‐de Vries equation and traveling wave solutions

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 6, Page 379-384, 2000., 2000
The three‐dimensional power Korteweg‐de Vries equation [ut+unux+uxxx] x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n = 1 and n = 2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson′s summation ...
Kenneth L. Jones
wiley   +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   +5 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   +5 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

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

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   +4 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

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

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

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