arXiv subjects

M. Senthilvelan

Publications and source records attributed to M. Senthilvelan.

At least 73 records · Page 4Linked to original sources

arXiv2016

Different kinds of chimera death states in nonlocally coupled oscillators

We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multi-chimera death state, type-I periodic chimera death (PCD) state and, type-II periodic chimera death (PCD) state. We also find that the number of periodic domains in both the types of PCD states exponentially decreases with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase approximation. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of multi-chimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.

nlin.CD↗

arXiv2016

The inverse problem of a mixed Liénard type nonlinear oscillator equation from symmetry perspective

In this paper, we discuss the inverse problem for a mixed Liénard type nonlinear oscillator equation $\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0$, where $f(x),\,g(x)$ and $h(x)$ are arbitrary functions of $x$. Very recently, we have reported the Lie point symmetries of this equation. By exploiting the interconnection between Jacobi last multiplier, Lie point symmetries and Prelle-Singer procedure we construct a time independent integral for the case exhibiting maximal symmetry from which we identify the associated conservative non-standard Lagrangian and Hamiltonian functions. The classical dynamics of the nonlinear oscillator is also discussed and certain special properties including isochronous oscillations are brought out.

nlin.SI↗

arXiv2016

Manipulating localized matter waves in multi-component Bose-Einstein condensates

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures, namely rogue waves, dark-and bright soliton-rogue wave, and rogue wave-breather-like wave for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Further we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single, two and three composite rogue waves for three component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.

nlin.PS↗

arXiv2015

Bi-$\cal{PT}$ symmetry in nonlinearly damped dynamical systems and tailoring $\cal{PT}$ regions with position dependent loss-gain profiles

We investigate the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear $\cal{PT}$-symmetric systems. We illustrate the nature of $\cal{PT}$-symmetry preservation and breaking with reference to a remarkable integrable scalar nonlinear system. In the two dimensional cases of such position dependent damped systems, we unveil the existence of a class of novel bi-$\cal{PT}$-symmetric systems which have two fold $\cal{PT}$ symmetries. We analyze the dynamics of these systems and show how symmetry breaking occurs, that is whether the symmetry breaking of the two $\cal{PT}$ symmetries occurs in pair or occurs one by one. The addition of linear damping in these nonlinearly damped systems induces competition between the two types of damping. This competition results in a $\cal{PT}$ phase transition in which the $\cal{PT}$ symmetry is broken for lower loss/gain strength and is restored by increasing the loss/gain strength. We also show that by properly designing the form of the position dependent damping, we can tailor the $\cal{PT}$-symmetric regions of the system.

nlin.PS↗

arXiv2015

Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains

We identify contact transformations which linearize the given equations in the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations to the same order. The identified contact transformations are not of Cole-Hopf type and are \emph {new} to the literature. The linearization of Abel chain of equations is also demonstrated explicitly for the first time. The contact transformations can be utilized to derive dynamical symmetries of the associated nonlinear ODEs. The wider applicability of identifying this type of contact transformations and the method of deriving dynamical symmetries by using them is illustrated through two dimensional generalizations of the Riccati and Abel chains as well.

nlin.SI↗

arXiv2015

On the non-$k$-separability of Dicke class of states and $N$-qudit W states

In this paper, we present the separability criteria to identify non-$k$-separability and genuine multipartite entanglement in mixed multipartite states using elements of density matrices. Our criteria can detect the non-$k$-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 $N$-qubit Dicke states with arbitrary excitations added with white noise and mixture of $N$-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.

quant-ph↗

arXiv2015

Impact of symmetry breaking in networks of globally coupled oscillators

We analyze the consequences of symmetry breaking in the coupling in a network of globally coupled identical Stuart-Landau oscillators. We observe that symmetry breaking leads to increased disorderliness in the dynamical behavior of oscillatory states and consequently results in a rich variety of dynamical states. Depending on the strength of the nonisochronicity parameter, we find various dynamical states such as amplitude chimera, amplitude cluster, frequency chimera and frequency cluster states. In addition we also find disparate transition routes to recently observed chimera death state in the presence of symmetry breaking even with global coupling. We also analytically verify the chimera death region which corroborates the numerical results. The above results are compared with that of the symmetry preserving case as well.

nlin.AO↗

arXiv2015

On certain analytical methods in finding integrable systems and their interconnections

In this paper, to begin with, we review six different analytical methods which are widely used to derive symmetries, integrating factors, multipliers, Darboux polynomials and integrals of second order nonlinear ordinary differential equations. We illustrate the algorithm behind each method by considering a nonlinear oscillator equation as an example. In the second part of this paper, we examine the interconnections between these methods. We establish a road map between extended Prelle-Singer procedure with all other methods cited above and thereby demonstrate the interplay between Lie point symmetries, $λ$-symmetries, adjoint symmetries, null forms, integrating factors, Darboux polynomials, and Jacobi multipliers of second order integrable ODEs. The interconnections are illustrated with the same example finally.

nlin.SI↗

arXiv2015

Symmetries of nonlinear ordinary differential equations: the modified Emden equation as a case study

Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries, hidden symmetries, nonlocal symmetries, $λ$-symmetries, adjoint symmetries and telescopic vector fields of a second-order ordinary differential equation. We also illustrate the algorithm involved in each method by considering a nonlinear oscillator equation as an example. The connections between (i) symmetries and integrating factors and (ii) symmetries and integrals are also discussed and illustrated through the same example. The interconnections between some of the above symmetries, that is (i) Lie point symmetries and $λ$-symmetries and (ii) exponential nonlocal symmetries and $λ$-symmetries are also discussed. The order reduction procedure is invoked to derive the general solution of the second-order equation.

nlin.SI↗

arXiv2015

Interconnections between various analytic approaches applicable to third-order nonlinear differential equations

We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ordinary differentiable equations (ODEs). We establish an important interconnection between extended Prelle-Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.

nlin.SI↗

arXiv2015

Criteria for non-$k$-separability of $n$-partite quantum states

We develop separability criteria to identify non-$k$-separability $(k = 2,3,\ldots,n)$ and genuine multipartite entanglement in different classes of mixed $n$-partite quantum states using elements of density matrices. With the help of these criteria, we detect non-$k$-separability in $n$-qudit GHZ and W states respectively added with white noise. We also discuss the experimental implementation of our criteria by means of local observables.

quant-ph↗

arXiv2015

On the separability criterion of bipartite states with certain non-Hermitian operators

We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix elements can be reformulated by the expectation values of these non-Hermitian operators and vice versa. We consider the condition of pure states and pure product states and rewrite them in terms of expectation values and density matrix elements respectively. We utilize expectation values of these operators to present the condition for separability of ${C}^d \otimes {C}^d$ bipartite states. With the help of our separability criterion we detect entanglement in certain classes of higher dimensional bipartite states.

quant-ph↗

arXiv2014

On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

We construct Darboux transformation of a coupled generalized nonlinear Schrödinger (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.

nlin.SI↗

arXiv2014

Manipulating matter-rogue waves and breathers in Bose-Einstein condensates

We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps, namely (i) time-independent expulsive trap, (ii) time-dependent monotonous trap and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second and third-order rogue waves transform into the first-order like rogue waves. We also analyze the density profiles of breather solutions. Here also we show that the shapes of the breathers change when we tune the strength of trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

nlin.SI↗

arXiv2014

On the characterization of breather and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schrödinger 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.

nlin.SI↗

arXiv2014

Generalized Darboux transformation and N-th order rogue wave solution of a general coupled nonlinear Schrödinger equations

We construct a generalized Darboux transformation (GDT) of a general coupled nonlinear Schrödinger (GCNLS) system. Using GDT method we derive a recursive formula and present determinant representations for N-th order rogue wave solution of this system. Using these representations we derive first, second and third order rogue wave solutions with certain free parameters. By varying these free parameters we demonstrate the formation of triplet, triangle and hexagonal patterns of rogue waves.

nlin.SI↗

arXiv2014

Dark solitons, Breathers and Rogue Wave Solutions of the Coupled Generalized Nonlinear Schrödinger Equations

We construct dark-dark solitons, general breather (GB), Akhmediev breather (AB), Ma soliton (MS) and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While the dark-dark solitons are captured in the defocusing regime of CGNLS system, the other solutions, namely GB, AB, MS and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak gets shrunk. Interestingly the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider RW solution as the starting point and derive AB, MS and GB in the reverse direction and show that the solutions obtained in both the directions match with each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.

nlin.SI↗

arXiv2014

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 $A_3$ and the $s$-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.

quant-ph↗