2 research outputs found
Numerical Solitons of Generalized Korteweg-de Vries Equations
We propose a numerical method for finding solitary wave solutions of
generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue
problem on an unbounded domain. The artificial boundary conditions are obtained
to make the domain finite. We specially discuss the soliton solutions of the
K(m, n) equation and KdV-K(m,n) equation. Furthermore for the mixed models of
linear and nonlinear dispersion, the collision behaviors of soliton-soliton and
soliton-antisoliton are observed.Comment: 9 pages, 4 figure
Self-similar Radiation from Numerical Rosenau-Hyman Compactons
The numerical simulation of compactons, solitary waves with compact support,
is characterized by the presence of spurious phenomena, as numerically-induced
radiation, which is illustrated here using four numerical methods applied to
the Rosenau-Hyman K(p,p) equation. Both forward and backward radiations are
emitted from the compacton presenting a self-similar shape which has been
illustrated graphically by the proper scaling. A grid refinement study shows
that the amplitude of the radiations decreases as the grid size does,
confirming its numerical origin. The front velocity and the amplitude of both
radiations have been studied as a function of both the compacton and the
numerical parameters. The amplitude of the radiations decreases exponentially
in time, being characterized by a nearly constant scaling exponent. An ansatz
for both the backward and forward radiations corresponding to a self-similar
function characterized by the scaling exponent is suggested by the present
numerical results.Comment: To be published in Journal of Computational Physic