arXiv subjects

K. Porsezian

Publications and source records attributed to K. Porsezian.

25 records · Page 2Linked to original sources

arXiv2013

Rotation of the Trajectories of Bright soliton and Realignment of Intensity Distribution in the Coupled Nonlinear Schrodinger Equation

We revisit the collisional dynamics of bright solitons in the coupled Nonlinear Schrodinger equation. We observe that apart from the intensity redistribution in the interaction of bright solitons, one also witnesses a rotation of the trajectories of bright solitons . The angle of rotation can be varied by suitably manipulating the Self-Phase Modulation (SPM) or Cross Phase Modulation (XPM) parameters.The rotation of the trajectories of the bright solitons arises due to the excess energy that is injected into the dynamical system through SPM or XPM. This extra energy not only contributes to the rotation of the trajectories, but also to the realignment of intensity distribution between the two modes. We also notice that the angular separation between the bright solitons can also manouvred suitably. The above results which exclude quantum superposition for the field vectors may have wider ramifications in nonlinear optics, Bose-Einstein condensates, Left Handed (LH) and Right Handed (RH) meta materials.

cond-mat.other↗

arXiv2013

Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation

In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describes the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter $γ_1$, denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by $γ_1$ are discussed in detail.

nlin.SI↗

arXiv2013

A generating mechanism for higher order rogue waves

We introduce a mechanism for generating higher order rogue waves (HRWs) of the nonlinear Schrödinger(NLS) equation: the progressive fusion and fission of $n$ degenerate breathers associated with a critical eigenvalue $λ_0$, creates an order $n$ HRW. By adjusting the relative phase of the breathers at the interacting area, it is possible to obtain different types of HRWs. The value $λ_0$ is a zero point of the eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order $n$ HRW.

nlin.SI↗

arXiv2013

Higher-Order Nonlinear Schrodinger equation with derivative non-Kerr nonlinear terms: A model for sub-10fs pulse propagation

We analytically solved the higher-order nonlinear Schrodinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and investigated explicitly bright and dark solitary wave solutions. Periodic wave solutions are also presented. The functional form of the bright and dark solitons presented are different from fundamental known sech(.) and tanh(.) respectively. We have estimated theoretically the size of the derivative non-Kerr nonlinear coefficients of the HNLS equation that agreed the reality of the waveguide made of highly nonlinear optical materials, could be used as the model parameters for sub-10fs pulse propagation.

nlin.SI↗

arXiv2013

Rogue waves of the Hirota and the Maxwell-Bloch equations

In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch(H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fibre and further generalize it to the matrix form of the $n$-fold Darboux transformation of this system. This $n$-fold Darboux transformation implies the determinant representation of $n$-th new solutions of $(E^{[n]},p^{[n]}, η^{[n]})$ generated from known solution of $(E, p,η)$. The determinant representation of $(E^{[n]},p^{[n]} ,η^{[n]})$ provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct bright and dark rogue wave solutions for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for $p\, and\, η$ has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing time and spatial parameters and changing other two unknown parameters $α$ and $β$, we generate a rogue wave shape for the first time.

nlin.SI↗

arXiv2012

Dynamics of matter-wave solutions of Bose-Einstein condensates in a homogeneous gravitational field

We find a matter-wave solution of Bose-Einstein condensates trapped in a harmonic-oscillator potential and subjected to a homogeneous gravitational field, by means of the extended tanhfunction method. This solution has as special cases the bright and dark solitons. We investigate the dynamics and the kinematics of these solutions, and the role of gravity is sketched. It is shown that these solutions can be generated and manipulated by controlling the s-wave scattering length, without changing the strengths of the magnetic and gravitational fields.

cond-mat.quant-gas↗

arXiv2008

Modulational instability of optical beams in photorefractive media in the presence of two wave and four wave mixing effects

Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained. In both the cases, the geometry is such that the effect of self-phase-modulation self-focusing is suppressed and only the holographic focusing nonlinearity is acting.

nlin.PS↗