200 research outputs found
An analysis of spatiotemporal localized solutions in the variable coefficients (3+1)-dimensional nonlinear Schr\"{o}dinger equation with six different forms of dispersion parameters
We construct spatiotemporal localized envelope solutions of a
(3+1)-dimensional nonlinear Schr\"{o}dinger equation with varying coefficients
such as dispersion, nonlinearity and gain parameters through similarity
transformation technique. The obtained localized rational solutions can serve
as prototypes of rogue waves in different branches of science. We investigate
the characteristics of constructed localized solutions in detail when it
propagates through six different dispersion profiles, namely constant, linear,
Gaussian, hyperbolic, logarithm and exponential. We also obtain expressions for
the hump and valleys of rogue wave intensity profiles for these six dispersion
profiles and study the trajectory of it in each case. Further, we analyze how
the intensity of another localized solution, namely breather, changes when it
propagates through the aforementioned six dispersion profiles. Our studies
reveal that these localized solutions co-exist with the collapsing solutions
which are already found in the (3+1)-dimensional nonlinear Schr\"{o}dinger
equation. The obtained results will help to understand the corresponding
localized wave phenomena in related fields.Comment: 32 pages, 17 figures, Accepted for publication in Chao
On the symmetries of a nonlinear non-polynomial oscillator
In this paper, we unearth symmetries of different types of a nonlinear
non-polynomial oscillator. The symmetries which we report here are
adjoint-symmetries, contact symmetries and telescopic vector fields. We also
obtain Jacobi last multipliers and Darboux polynomials as a by-product of our
procedure. All the aforementioned quantities are derived from a Theorem proved
by Muriel and Romero. The procedure which we present here is applicable to a
class of nonlinear oscillator equations.Comment: 15 pages, submitted for publicatio
On the non--separability of Dicke class of states and -qudit W states
In this paper, we present the separability criteria to identify
non--separability and genuine multipartite entanglement in mixed
multipartite states using elements of density matrices. Our criteria can detect
the non--separability of Dicke class of states, anti W states and mixtures
thereof and higher dimensional W class of states. We then investigate the
performance of our criteria by considering -qubit Dicke states with
arbitrary excitations added with white noise and mixture of -qudit W state
with white noise. We also study the robustness of our criteria against white
noise. Further, we demonstrate that our criteria are experimentally
implementable by means of local observables such as Pauli matrices and
generalized Gell-Mann matrices.Comment: 19 pages, 8 figures, accepted for publication in IJT
On the generalized intelligent states and certain related nonclassical states of a quantum exactly solvable nonlinear oscillator
We construct nonlinear coherent states or f-deformed coherent states for a
nonpolynomial nonlinear oscillator which can be considered as placed in the
middle between the harmonic oscillator and the isotonic oscillator (Cari\~nena
J F et al, J. Phys. A: Math. Theor. 41, 085301 (2008)). The deformed
annihilation and creation operators which are required to construct the
nonlinear coherent states in the number basis are obtained from the solution of
the Schr\"odinger equation. Using these operators, we construct generalized
intelligent states, nonlinear coherent states, Gazeau-Klauder coherent states
and the even and odd nonlinear coherent states for this newly solvable system.
We also report certain nonclassical properties exhibited by these nonlinear
coherent states. In addition to the above, we consider position dependent mass
Schr\"odinger equation associated with this solvable nonlinear oscillator and
construct nonlinear coherent states, Gazeau-Klauder coherent states and the
even and odd nonlinear coherent states for it. We also give explicit
expressions of all these nonlinear coherent states by considering a mass
profile which is often used for studying transport properties in
semiconductors.Comment: 22 pages, 3 figures, Accepted for Publication in Journal of Physics
A: Mathematical and Theoretica
An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator
In this paper, we construct nonlinear coherent states for the generalized
isotonic oscillator and study their non-classical properties in-detail. By
transforming the deformed ladder operators suitably, which generate the
quadratic algebra, we obtain Heisenberg algebra. From the algebra we define two
non-unitary and an unitary displacement type operators. While the action of one
of the non-unitary type operators reproduces the original nonlinear coherent
states, the other one fails to produce a new set of nonlinear coherent states
(dual pair). We show that these dual states are not normalizable. For the
nonlinear coherent states, we evaluate the parameter and examine the
non-classical nature of the states through quadratic and amplitude-squared
squeezing effect. Further, we derive analytical formula for the -function,
-function and the Wigner function for the nonlinear coherent states. All of
them confirm the non-classicality of the nonlinear coherent states. In addition
to the above, we obtain the harmonic oscillator type coherent states from the
unitary displacement operator.Comment: To appear in J. Math. Phys., (2012
Photon modulated coherent states of a generalized isotonic oscillator by Weyl ordering and their non-classical properties
We construct photon modulated coherent states of a generalized isotonic
oscillator by expanding the newly introduced superposed operator through Weyl
ordering method. We evaluate the parameter and the -parameterized
quasi probability distribution function to confirm the non - classical nature
of the states. We also calculate the identities related with the quadrature
squeezing to explore the squeezing property of the states. Finally, we
investigate the fidelity between the photon modulated coherent states and
coherent states to quantify the non-Gaussianity of the states. The constructed
states and their associated non - classical properties will add further
knowledge on the potential.Comment: To appear in Int. J. Theor. Phys., 201
On the characterization of breather and rogue wave solutions of an inhomogeneous nonlinear Schr\"odinger equation
We construct breather and rogue wave solutions of a variable coefficient
nonlinear Schr\"odinger equation with an external linear potential. This
generalized model describes the nonlinear wave propagation in an inhomogeneous
plasma/medium. We derive several localized solutions including Ma breather,
Akhmediev breather, two-breather and rogue wave solutions of this model and
show how the inhomogeneity of space modifies the shape and orientation of these
localized structures. We also depict the trajectories of the inhomogeneous
rogue wave. Our results may be useful for controlling plasmonic energy along
the plasma surface.Comment: 15 pages, 11 figures, submitted for publication. arXiv admin note:
text overlap with arXiv:1407.270
On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schr\"odinger equations
We construct Darboux transformation of a coupled generalized nonlinear
Schr\"odinger (CGNLS) equations and obtain exact analytic expressions of
breather and rogue wave solutions. We also formulate the conditions for
isolating these solutions. We show that the rogue wave solution can be found
only when the four wave mixing parameter becomes real. We also investigate the
modulation instability of the steady state solution of CGNLS system and
demonstrate that it can occur only when the four wave mixing parameter becomes
real. Our results give an evidence for the connection between the occurrence of
rogue wave solution and the modulation instability.Comment: 14 pages, 3 figures, To appear in Wave Motio
Nonstandard bilinearization of -invariant nonlocal nonlinear Schr\"{o}dinger equation: Bright soliton solutions
In this paper, we succeed to bilinearize the -invariant nonlocal
nonlinear Schr\"{o}dinger (NNLS) equation through a nonstandard procedure and
present more general bright soliton solutions. We achieve this by bilinearizing
both the NNLS equation and its associated parity transformed complex conjugate
equation in a novel way. The obtained one and two soliton solutions are
invariant under combined space and time reversal transformations and are more
general than the known ones. Further, by considering the two-soliton solution
we bring out certain novel interaction properties of the -invariant
multi-soliton solutions.Comment: 13 pages, 2 figures, Accepted for Publication in Physics Letters
Akhmediev breathers, Ma solitons and general breathers from rogue waves: A case study in Manakov system
We present explicit forms of general breather (GB), Akhmediev breather (AB),
Ma soliton (MS) and rogue wave (RW) solutions of the two component nonlinear
Schr\"{o}dinger (NLS) equation, namely Manakov equation. We derive these
solutions through two different routes. In the forward route we first construct
a suitable periodic envelope soliton solution to this model from which we
derive GB, AB, MS and RW solutions. We then consider the RW solution as the
starting point and derive AB, MS and GB in the reverse direction. The second
approach has not been illustrated so far for the two component NLS equation.
Our results show that the above rational solutions of the Manakov system can be
derived from the standard scalar nonlinear Schr\"{o}dinger equation with a
modified nonlinearity parameter. Through this two way approach we establish a
broader understanding of these rational solutions which will be of interest in
a variety of situations.Comment: 11 pages, 4 figure
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