213 research outputs found
Inelastic interaction of nearly equal solitons for the BBM equation
This paper is concerned with the interaction of two solitons of nearly equal
speeds for the (BBM) equation. This work is an extension of the results
obtained in arXiv:0910.3204 by the same authors, addressing the same question
for the quartic (gKdV) equation. First, we prove that the two solitons are
preserved by the interaction and that for all time they are separated by a
large distance, as in the case of the integrable (KdV) equation in this regime.
Second, we prove that the collision is not perfectly elastic, except in the
integrable case (i.e. in the limiting case of the (KdV) equation)
Asymptotic soliton like solutions to the singularly perturbed Benjamin-Bona-Mahony equation with variable coefficients
The paper deals with a problem of asymptotic soliton like solutions to the
Benjamin-Bona-Mahony (BBM) equaion with a small parameter at the highest
derivative and variable coefficients depending on the variables , as
well as a small parameter. There is proposed an algorithm of constructing the
solutions and there are proved theorems on accuracy with which the solutions
satisfy the BBM equation.Comment: 19 pages, 44 reference
Description of the inelastic collision of two solitary waves for the BBM equation
We prove that the collision of two solitary waves of the BBM equation is
inelastic but almost elastic in the case where one solitary wave is small in
the energy space. We show precise estimates of the nonzero residue due to the
collision. Moreover, we give a precise description of the collision phenomenon
(change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.
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
Elliptic solutions to a generalized BBM equation
An approach is proposed to obtain some exact explicit solutions in terms of
the Weierstrass' elliptic function to a generalized Benjamin-Bona-Mahony
(BBM) equation. Conditions for periodic and solitary wave like solutions can be
expressed compactly in terms of the invariants of . The approach unifies
recently established ad-hoc methods to a certain extent. Evaluation of a
balancing principle simplifies the application of this approach.Comment: 11 pages, 2 tables, submitted to Phys. Lett.
Reliable Study of Nonhomogeneous BBM Equation with Time-Dependent Coefficients by the Modified Sine-Cosine Method
The modified sine-cosine method is an efficient and powerful mathematical tool in finding exact traveling wave solutions to nonlinear partial differential equations (NLPDEs) with time-dependent coefficients. In this paper, the proposed approach is applied to study a nonhomogeneous generalized form of Benjamin-Bona-Mahony (BBM) equation with time-dependent coefficients. Explicit traveling wave solutions of the equation are obtained under certain constraints on the coefficient functions
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