264 research outputs found
On certain new exact solutions of a diffusive predator-prey system
We construct exact solutions for a system of two nonlinear partial
differential equations describing the spatio-temporal dynamics of a
predator-prey system where the prey per capita growth rate is subject to the
Allee effect. Using the expansion method, we derive
exact solutions to this model for two different wave speeds. For each wave
velocity we report three different forms of solutions. We also discuss the
biological relevance of the solutions obtained.Comment: Accepted for Publication in Commun. Nonlin. Sci. Num. Sim. (2012
On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients
We construct vector rogue wave solutions of the two-dimensional two coupled
nonlinear Schr\"{o}dinger equations with distributed coefficients, namely
diffraction, nonlinearity and gain parameters through similarity transformation
technique. We transform the two-dimensional two coupled variable coefficients
nonlinear Schr\"{o}dinger equations into Manakov equation with a constraint
that connects diffraction and gain parameters with nonlinearity parameter. We
investigate the characteristics of the constructed vector rogue wave solutions
with four different forms of diffraction parameters. We report some interesting
patterns that occur in the rogue wave structures. Further, we construct vector
dark rogue wave solutions of the two-dimensional two coupled nonlinear
Schr\"{o}dinger equations with distributed coefficients and report some novel
characteristics that we observe in the vector dark rogue wave solutions.Comment: Accepted for publication in The European Physical Journal
Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates
We construct rogue wave and breather solutions of a quasi-two-dimensional
Gross-Pitaevskii equation with a time-dependent interatomic interaction and
external trap. We show that the trapping potential and an arbitrary functional
parameter that present in the similarity transformation should satisfy a
constraint for the considered equation to be integrable and yield the desired
solutions. We consider two different forms of functional parameters and
investigate how the density of the rogue wave and breather profiles vary with
respect to these functional parameters. We also construct vector localized
solutions of a two coupled quasi-two-dimensional Bose-Einstein condensate
system. We then investigate how the vector localized density profiles modify in
the constant density background with respect to the functional parameters. Our
results may help to manipulate matter rogue waves experimentally in the
two-dimensional Bose-Einstein condensate systems.Comment: 16 pages, Published in Eur. Phys. J.
Dissipationless shock waves in repulsive Bose-Einstein condensates
We consider formation of dissipationless shock waves in Bose-Einstein
condensates with repulsive interaction between atoms. It is shown that big
enough initial inhomogeneity of density leads to wave breaking phenomenon
followed by generation of a train of dark solitons. Analytical theory is
confirmed by numerical simulations.Comment: 7 pages, 5 figures in JPG forma
Asymptotic dynamics of short-waves in nonlinear dispersive models
The multiple-scale perturbation theory, well known for long-waves, is
extended to the study of the far-field behaviour of short-waves, commonly
called ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation
can propagates short-waves. This result contradict the Benjamin hypothesis that
short-waves tends not to propagate in this model and close a part of the old
controversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine
equations. We shown that a nonlinear (quadratic) Klein-Gordon type equation
substitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation
of long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon
equations are understood as an all orders asymptotic behaviour of short-waves.
It is proved that the antikink solution of phi-4 model which was never obtained
perturbatively can be obtained by perturbation expansion in the wave-number k
in the short-wave limit.Comment: to appears in Physical Review E. 4 pages, revtex file
Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation
By considering the long-wave limit of the regularized long wave (RLW)
equation, we study its multiple-time higher-order evolution equations. As a
first result, the equations of the Korteweg-de Vries hierarchy are shown to
play a crucial role in providing a secularity-free perturbation theory in the
specific case of a solitary-wave solution. Then, as a consequence, we show that
the related perturbative series can be summed and gives exactly the
solitary-wave solution of the RLW equation. Finally, some comments and
considerations are made on the N-soliton solution, as well as on the
limitations of applicability of the multiple scale method in obtaining uniform
perturbative series.Comment: 15 pages, RevTex, no figures (to appear in Phys. Rev. E
Solitons in tunnel-coupled repulsive and attractive condensates
We study solitons in the condensate trapped in a double-well potential with
far-separated wells, when the s-wave scattering length has different signs in
the two parts of the condensate. By employing the coupled-mode approximation it
is shown that there are unusual stable bright solitons in the condensate, with
the larger share of atoms being gathered in the repulsive part. Such unusual
solitons derive their stability from the quantum tunneling and correspond to
the strong coupling between the parts of the condensate. The ground state of
the system, however, corresponds to weak coupling between the condensate parts,
with the larger share of atoms being gathered in the attractive part of the
condensate.Comment: LaTex, 23 pages, 6 figures; revised version; to appear in Physical
Review
Mixed-isotope Bose-Einstein condensates in Rubidium
We consider the ground state properties of mixed Bose-Einstein condensates of
87Rb and 85Rb atoms in the isotropic pancake trap, for both signs of the
interspecies scattering length. In the case of repulsive interspecies
interaction, there are the axially-symmetric and symmetry-breaking ground
states. The threshold for the symmetry breaking transition, which is related to
appearance of a zero dipole-mode, is found numerically. For attractive
interspecies interactions, the two condensates assume symmetric ground states
for the numbers of atoms up to the collapse instability of the mixture.Comment: Revised; 21 pages, 5 figures, submitted to Physical Review
Linearizability of the Perturbed Burgers Equation
We show in this letter that the perturbed Burgers equation is equivalent, through a near-identity transformation and
up to order \epsilon, to a linearizable equation if the condition is satisfied. In the case this
condition is not fulfilled, a normal form for the equation under consideration
is given. Then, to illustrate our results, we make a linearizability analysis
of the equations governing the dynamics of a one-dimensional gas.Comment: 10 pages, RevTeX, no figure
Dissipative Boussinesq System of Equations in the B\'enard-Marangoni Phenomenon
By using the long-wave approximation, a system of coupled evolution equations
for the bulk velocity and the surface perturbations of a B\'enard-Marangoni
system is obtained. It includes nonlinearity, dispersion and dissipation, and
it can be interpreted as a dissipative generalization of the usual Boussinesq
system of equations. As a particular case, a strictly dissipative version of
the Boussinesq system is obtained. Finnaly, some speculations are made on the
nature of the physical phenomena described by this system of equations.Comment: 15 Pages, REVTEX (Version 3.0), no figure
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