340 research outputs found
Phase modulated solitary waves controlled by bottom boundary condition
A forced KdV equation is derived to describe weakly nonlinear, shallow water
surface wave propagation over non trivial bottom boundary condition. We show
that different functional forms of bottom boundary conditions self-consistently
produce different forced kdV equations as the evolution equations for the free
surface. Solitary wave solutions have been analytically obtained where phase
gets modulated controlled by bottom boundary condition whereas amplitude
remains constant.Comment: 13 pages, 6 figures, Accepted in Physical Review
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Quantum corrections to nonlinear ion acoustic wave with Landau damping have
been computed using Wigner equation approach. The dynamical equation governing
the time development of nonlinear ion acoustic wave with semiclassical quantum
corrections is shown to have the form of higher KdV equation which has higher
order nonlinear terms coming from quantum corrections, with the usual classical
and quantum corrected Landau damping integral terms.
The conservation of total number of ions is shown from the evolution
equation. The decay rate of KdV solitary wave amplitude due to presence of
Landau damping terms has been calculated assuming the Landau damping parameter
to be of the same order of the quantum
parameter . The amplitude is shown to
decay very slowly with time as determined by the quantum factor .Comment: 9 pages, 1 figur
Bending of solitons in weak and slowly varying inhomogeneous plasma
Bending of solitons in two dimensional plane is presented in the presence of
weak and slowly varying inhomogeneous ion density for the propagation of ion
acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using
reductive perturbation technique, a modified Kadomtsev- Petviashvili equation
is obtained with a chosen unperturbed ion density profile. Exact solution of
the equation shows that the phase of the solitary wave gets modified by a
function related to the unperturbed inhomogeneous ion density causing the
soliton to bend in the two dimensional plane, whereas the amplitude of the
soliton remaining constantComment: 10 pages, 11 figure
Jeans Instability in a viscoelastic fluid
The well known Jeans instability is studied for a viscoelastic, gravitational
fluid using generalized hydrodynamic equations of motions. It is found that the
threshold for the onset of instability appears at higher wavelengths in a
viscoelastic medium. Elastic effects playing a role similar to thermal pressure
are found to lower the growth rate of the gravitational instability. Such
features may manifest themselves in matter constituting dense astrophysical
objects.Comment: 10 pages, 4 figure
A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma
A new, completely integrable, two dimensional evolution equation is derived
for an ion acoustic wave propagating in a magnetized, collisionless plasma. The
equation is a multidimensional generalization of a modulated wavepacket with
weak transverse propagation, which has resemblance to nonlinear Schrodinger
(NLS) equation and has a connection to Kadomtsev-Petviashvili equation through
a constraint relation. Higher soliton solutions of the equation are derived
through Hirota bili- nearization procedure, and an exact lump solution is
calculated exhibiting 2D structure. Some mathe- matical properties
demonstrating the completely integrable nature of this equation are described.
Modulational instability using nonlinear frequency correction is derived, and
the corresponding growth rate is calculated, which shows the directional
asymmetry of the system. The discovery of this novel (2{\th}1) dimensional
integrable NLS type equation for a magnetized plasma should pave a new
direction of research in the field.Comment: 11 pages, 8 figure
Controlling near shore nonlinear surging waves through bottom boundary conditions
Instead of taking the usual passive view for warning of near shore surging
waves including extreme waves like tsunamis, we aim to study the possibility of
intervening and controlling nonlinear surface waves through the feedback
boundary effect at the bottom. It has been shown through analytic result that
the controlled leakage at the bottom may regulate the surface solitary wave
amplitude opposing the hazardous variable depth effect. The theoretical results
are applied to a real coastal bathymetry in India.Comment: 19 pages, 12 figure
Kelvin-Helmholtz Instability in non-Newtonian Complex Plasma
The Kelvin-Helmholtz (KH) instability is studied in a non-Newtonian dusty
plasma with an experimentally verified model [Phys. Rev. Lett. {\bf 98}, 145003
(2007)] of shear flow rate dependent viscosity. The shear flow profile used
here is a parabolic type bounded flow. Both the shear thinning and shear
thickening properties are investigated in compressible as well as
incompressible limits using a linear stability analysis. Like the stabilizing
effect of compressibility on the KH instability, the non-Newtonian effect in
shear thickening regime could also suppress the instability but on the
contrary, shear thinning property enhances it. A detailed study is reported on
the role of non-Newtonian effect on KH instability with conventional dust fluid
equations using standard eigenvalue analysis.Comment: 13 pages, 4 figure
Shear Waves in an inhomogeneous strongly coupled dusty plasma
The properties of electrostatic transverse shear waves propagating in a
strongly coupled dusty plasma with an equilibrium density gradient are examined
using the generalized hydrodynamic equation. In the usual kinetic limit, the
resulting equation has similarity to zero energy Schrodinger's equation. This
has helped in obtaining some exact eigenmode solutions in both cartesian and
cylindrical geometries for certain nontrivial density profiles. The
corresponding velocity profiles and the discrete eigenfrequencies are obtained
for several interesting situations and their physics discussed.Comment: 10 pages, 4 figure
Viscosity gradient driven instability of `shear mode' in a strongly coupled plasma
The influence of viscosity gradient (due to shear flow) on low frequency
collective modes in strongly coupled dusty plasma is analyzed. It is shown that
for a well known viscoelastic plasma model, the velocity shear dependent
viscosity leads to an instability of the shear mode. The inhomogeneous viscous
force and velocity shear coupling supply the free energy for the instability.
The combined strength of shear flow and viscosity gradient wins over any
stabilizing force and makes the shear mode unstable. Implication of such a
novel instability and its applications are briefly outlined.Comment: 9 pages, 2 figure
Nonlinear Shear Wave in a Non Newtonian Visco-elastic Medium
An analysis of nonlinear transverse shear wave has been carried out on
non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The
nonlinear viscoelastic behavior is introduced through velocity shear dependence
of viscosity coefficient by well known Carreau -Bird model. The dynamical
feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU)
problem. Numerical solution has been obtained which shows that initial periodic
solutions reoccur after passing through several patterns of periodic waves. A
possible explanation for this periodic solution is given by constructing
modified Korteweg de Vries (mKdV) equation. This model has application from
laboratory to astrophysical plasmas as well as biological systems.Comment: 5 pages, 2 figure
- β¦