arXiv subjects

C. N. Kumar

Publications and source records attributed to C. N. Kumar.

12 recordsLinked to original sources

arXiv2021

Phase modulated domain walls and dark solitons for surface gravity waves

We report theoretical prediction of exact localized solutions for dynamics of surface gravity waves, at the critical point kh=1.363, modelled by higher-order nonlinear Schrodinger equation. The model possess domain walls (kink solitons) and dark solitons modulated through different phase profiles. The parametric domains are delineated for the existence of soliton solutions. The effect of wave parameters have been discussed on the amplitude of surface gravity waves. Our work is motivated by Tsitoura et al. [1], on experimental and analytical observation of phase domain walls for deep water surface gravity waves modelled by nonlinear Schrodinger equation.

nlin.PS↗

arXiv2020

Chirped nonlinear resonant states in femtosecond fiber optics

We show the existence of nonlinear resonant states in a higher-order nonlinear Schrödinger model that appertains to the wave propagation in femtosecond fiber optics, under certain parametric regime. These nonlinear resonant states are analytically illustrated in terms of Gaussian beams, Airy beams, and periodic beams that resulted due to the presence of quadratic, linear, and constant type of `smart' potentials, respectively, of the ensuing model. Interestingly, the nonlinear chirp associated with each of these novel resonant states can be efficiently controlled, by varying the self-steepening term and self-frequency shift. Furthermore, we have conducted numerical experiments corroborative of our analytical predictions.

nlin.PS↗

arXiv2020

Generation and controlling of ultrashort self-similar solitons and rogue waves in inhomogeneous optical waveguide

We present exact bright, dark and rogue soliton solutions of generalized higherorder nonlinear Schrodinger equation, describing the ultrashort beam propagation in tapered waveguide amplifier, via a similarity transformation connected with the constant-coefficient Sasa-Satsuma and Hirota equations. Our exact analysis takes recourse to identify the allowed tapering profile in conjunction with appropriate gain function which corresponds to PT-symmetric waveguide. We extend our analysis to study the effect of tapering profiles and higher-order terms on the evolution of self-similar waves and thus enabling one to control the self-similar wave structure and dynamical behavior.

nlin.PS↗

arXiv2020

Chirped Lambert W-kink solitons of the complex cubic-quintic Ginzburg-Landau equation with intrapulse Raman scattering

In this paper, an exact explicit solution for the complex cubic-quintic Ginzburg-Landau equation is obtained, by using Lambert W function or omega function. More pertinently, we term them as Lambert W-kink-type solitons, begotten under the influence of intrapulse Raman scattering. Parameter domains are delineated in which these optical solitons exit in the ensuing model. We report the effect of model coefficients on the amplitude of Lambert W-kink solitons, which enables us to control efficiently the pulse intensity and hence their subsequent evolution. Also, moving fronts or optical shock-type solitons are obtained as a byproduct of this model. We explicate the mechanism to control the intensity of these fronts, by fine tuning the spectral filtering or gain parameter. It is exhibited that the frequency chirp associated with these optical solitons depends on the intensity of the wave and saturates to a constant value as the retarded time approaches its asymptotic value.

nlin.PS↗

arXiv2020

Controlled self-similar matter waves in PT-symmetric waveguide

We study the dynamics of Bose-Einstein condensate coupled to a waveguide with parity-time symmetric potential in the presence of quadratic-cubic nonlinearity modelled by Gross-Pitaevskii equation with external source. We employ the self-similar technique to obtain matter wave solutions, such as bright, kinktype, rational dark and Lorentzian-type self-similar waves for this model. The dynamical behavior of self-similar matter waves can be controlled through variation of trapping potential, external source and nature of nonlinearities present in the system.

nlin.PS↗

arXiv2015

Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

We have investigated the ($2+1$)-dimensional variable coefficient coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation (SPM) and cross-phase modulation (XPM) coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers and rogue waves as different solutions.

nlin.PS↗

arXiv2015

Unbreakable $\mathcal{PT}$ symmetry of exact solitons supported by transversally modulated nonlinearity acting as a psuedopotential

We demonstrate analytically and numerically the existence of exact solitons in the form of double-kink and fractional-transform, supported by a symmetric transversally modulated defocusing nonlinearity acting as a psuedopotential combined with an antisymmetric gain-loss profile. We explicate here that the $\mathcal{PT}$ symmetry is never broken in the dynamical system under study, even in the absence of any symmetric modulation of linear refractive-index, and the transversally modulated defocusing nonlinearity comes in the way as a requirement to establish the ensuing $\mathcal{PT}$ symmetry.

nlin.PS↗

arXiv2014

A method to solve nonlinear Schrödinger equation using Riccati equation

A method to find exact solutions to nonlinear Schrödinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati equation. Generalisation of several known solutions is found using this method, in case of nonlinear Schrödinger equation defined on a line. This method also yields non-singular and singular vortex solutions, when applied to nonlinear Schrödinger equation on a plane.

nlin.SI↗

arXiv2014

Few-cycle optical solitary waves in cascaded-quadratic-cubic-quintic nonlinear media

We study the propagation of few-cycle optical solitary waves in a nonlinear media under the combined action of quadratic, cubic and quintic nonlinearities in a large phase-mismatched second harmonic (SHG) process. Exact bright and dark soliton solutions to the nonlinear evolution equation for cascaded quadratic media beyond the slowly varying envelope approximations is reported. The analytical solutions obtained are verified through numerical simulations.

physics.optics↗

arXiv2009

Density excitations of a harmonically trapped ideal gas

The dynamic structure factor of a harmonically trapped Bose gas has been calculated well above the Bose-Einstein condensation temperature by treating the gas cloud as a canonical ensemble of noninteracting classical particles. The static structure factor is found to vanish as wavenumber squared in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction force to study the dynamic structure factor. A significant temperature dependence of the density-fluctuation spectra is found. The Debye-Waller factor has been calculated for the trapped thermal cloud as function of wavenumber and of particle number. A substantial difference is found between clouds of small and large particle number.

cond-mat.quant-gas↗

arXiv1995

Exact Solutions To The Generalized Lienard Equations

Many new solitary wave solutions of the recently studied Lienard equation are obtained by mapping it to the field equation of the $ϕ^6-$field theory. Further, it is shown that the exact solutions of the Lienard equation are also the exact solutions of the various perturbed soliton equations. Besides, we also consider a one parameter family of generalised Lienard equations and obtain exact solitary wave solutions of these equations and show that these are also the exact solutions of the various other generalised nonlinear equations.

hep-th↗

arXiv1994

New Sets of Kink Bearing Hamiltonians

Given a kink bearing Hamiltonian, Isospectral Hamiltonian approach is used in generating new sets of Hamiltonains which also admit kink solutions. We use Sine-Gordon model as a example and explicitly work out the new sets of potentials and the solutions.

patt-sol↗