62 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
Traveling waves and Compactons in Phase Oscillator Lattices
We study waves in a chain of dispersively coupled phase oscillators. Two
approaches -- a quasi-continuous approximation and an iterative numerical
solution of the lattice equation -- allow us to characterize different types of
traveling waves: compactons, kovatons, solitary waves with exponential tails as
well as a novel type of semi-compact waves that are compact from one side.
Stability of these waves is studied using numerical simulations of the initial
value problem.Comment: 22 pages, 25 figure
On a hierarchy of nonlinearly dispersive generalized KdV equations
We propose a hierarchy of nonlinearly dispersive generalized Korteweg--de
Vries (KdV) evolution equations based on a modification of the Lagrangian
density whose induced action functional the KdV equation extremizes. It is
shown that two recent nonlinear evolution equations describing wave propagation
in certain generalized continua with an inherent material length scale are
members of the proposed hierarchy. Like KdV, the equations from the proposed
hierarchy possess Hamiltonian structure. Unlike KdV, however, the solutions to
these equations can be compact (i.e., they vanish outside of some open
interval) and, in addition, peaked. Implicit solutions for these peaked,
compact traveling waves ("peakompactons") are presented.Comment: 6 pages, 1 figure; to appear in the Proceedings of the Estonian
Academy of Science
Compactons and kink-like solutions of BBM-like equations by means of factorization
In this work, we study the Benjamin-Bona-Mahony like equations with a fully
nonlinear dispersive term by means of the factorization technique. In this way
we find the travelling wave solutions of this equation in terms of the
Weierstrass function and its degenerated trigonometric and hyperbolic forms.
Then, we obtain the pattern of periodic, solitary, compacton and kink-like
solutions. We give also the Lagrangian and the Hamiltonian, which are linked to
the factorization, for the nonlinear second order ordinary differential
equations associated to the travelling wave equations.Comment: 10 pages, 8 figure
- …