arXiv subjects

Debananda Chakraborty

Publications and source records attributed to Debananda Chakraborty.

11 recordsLinked to original sources

arXiv2026

Transition to spatiotemporal chaos with multiple colliding pulse sequences of the nonlinear Schr\"odinger equation

We present the first demonstration of transition to spatiotemporal chaos with multiple colliding pulse sequences in systems described by perturbed cubic nonlinear Schr\"odinger (NLS) equations. For this purpose, we consider propagation of multiple sequences of optical pulses in two distinct types of nonlinear waveguide arrays with cubic gain and loss. By employing a perturbation theory for NLS solitons, we show that the dynamics of pulse energies in the waveguide array systems is described by generalized Lotka-Volterra (LV) models, which exhibit dissipative chaos in a wide region in parameter space. We test the LV models' predictions for chaotic dynamics of pulse energies by extensive numerical simulations with perturbed systems of coupled-NLS equations. We find excellent agreement between the results of the LV and coupled-NLS models for energy dynamics in both types of waveguide array systems, despite the strong pulse pattern distortions and the strongly nonlinear nature of the dynamics.

nlin.PS↗

arXiv2024

Stabilizing optical solitons by frequency-dependent linear gain-loss and the collisional Raman frequency shift

We study transmission stabilization of optical solitons against emission of radiation in nonlinear optical waveguides in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. We first show how the collisional Raman frequency shift perturbation arises in three different physical setups. We then show by numerical simulations with a perturbed nonlinear Schrödinger (NLS) model that transmission in waveguides with weak frequency-independent linear gain is unstable. The radiative instability is stronger than the radiative instabilities that were observed in earlier studies for soliton transmission in the presence of weak linear gain, cubic loss, and various frequency-shifting physical mechanisms. In particular, the Fourier spectrum of the radiation is significantly more spiky and broadband than the radiation's Fourier spectra in earlier studies. Moreover, we demonstrate by numerical simulations with another perturbed NLS model that transmission in waveguides with weak frequency-dependent linear gain-loss, cubic loss, and the collisional Raman frequency shift is stable. Despite the stronger radiative instability in the corresponding waveguide setup with weak linear gain, stabilization occurs via the same generic mechanism that was suggested in earlier studies. More precisely, the collisional Raman frequency shift experienced by the soliton leads to the separation of the soliton's and the radiation's Fourier spectra, while the frequency-dependent linear gain-loss leads to efficient suppression of radiation emission. Thus, our study demonstrates the robustness of the proposed generic soliton stabilization method, which is based on the interplay between perturbation-induced shifting of the soliton's frequency and frequency-dependent linear gain-loss.

nlin.PS↗

arXiv2023

Stabilizing solitons of the cubic-quintic nonlinear Schrödinger equation by frequency-dependent linear gain-loss and delayed Raman response

We demonstrate transmission stabilization against radiation emission by frequency-dependent linear gain-loss and perturbation-induced frequency shifting for solitons of the cubic-quintic nonlinear Schrödinger (CQNLS) equation. We consider soliton propagation in a nonlinear optical waveguide with focusing cubic nonlinearity, defocusing quintic nonlinearity, and dissipative perturbations due to weak frequency-dependent linear gain-loss, cubic loss, and delayed Raman response. The frequency shifting is induced by delayed Raman response. Our perturbation analysis and numerical simulations with the perturbed CQNLS equation show that transmission stabilization with CQNLS solitons is indeed possible, and in this way provide the first demonstration of the stabilization method for solitons of a nonintegrable nonlinear wave model. Moreover, we find that transmission stabilization with energetic CQNLS solitons is realized with significantly smaller frequency shifts and pulse distortion compared with stabilization with energetic solitons of the cubic nonlinear Schrödinger equation. Therefore, our study also demonstrates that stabilization of energetic solitons by the method is significantly improved by the presence of defocusing quintic nonlinearity.

nlin.PS↗

arXiv2019

Radiation dynamics in fast soliton collisions in the presence of cubic loss

We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schrödinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a perturbation technique with two small parameters: the cubic loss coefficient $ε_{3}$ and the reciprocal of the group velocity difference $1/β$. The agreement between the perturbation theory predictions and the results of numerical simulations with the full coupled-NLS propagation model is very good for large $β$ values, and is good for intermediate $β$ values. Additional numerical simulations with four simplified NLS models show that the differences between perturbation theory and simulations for intermediate $β$ values are due to the effects of Kerr nonlinearity on interpulse interaction in the collision. Thus, our study demonstrates that the perturbation technique that was originally developed to study radiation dynamics in fast soliton collisions in the presence of conservative perturbations can also be employed for soliton collisions in the presence of dissipative perturbations.

nlin.PS↗

arXiv2018

Enhancement of transmission quality in soliton-based optical waveguide systems by frequency dependent linear gain-loss and the Raman self-frequency shift

We study transmission stabilization against radiation emission in soliton-based nonlinear optical waveguides with weak linear gain-loss, cubic loss, and delayed Raman response. We show by numerical simulations with perturbed nonlinear Schrödinger propagation models that transmission quality in waveguides with frequency independent linear gain and cubic loss is not improved by the presence of delayed Raman response due to the lack of an efficient mechanism for suppression of radiation emission. In contrast, we find that the presence of delayed Raman response leads to significant enhancement of transmission quality in waveguides with frequency dependent linear gain-loss and cubic loss. Enhancement of transmission quality in the latter waveguides is enabled by the separation of the soliton's spectrum from the radiation's spectrum due to the Raman-induced self-frequency shift and by efficient suppression of radiation emission due to the frequency dependent linear gain-loss. Further numerical simulations demonstrate that the enhancement of transmission quality in waveguides with frequency dependent linear gain-loss, cubic loss, and delayed Raman response is similar to transmission quality enhancement in waveguides with linear gain, cubic loss, and guiding filters with a varying central frequency.

physics.optics↗

arXiv2017

Large stable oscillations due to Hopf bifurcations in amplitude dynamics of colliding soliton sequences

We demonstrate that the amplitudes of optical solitons in nonlinear multisequence optical waveguide coupler systems with weak linear and cubic gain-loss exhibit large stable oscillations along ultra-long distances. The large stable oscillations are caused by supercritical Hopf bifurcations of the equilibrium states of the Lotka-Volterra (LV) models for dynamics of soliton amplitudes. The predictions of the LV models are confirmed by numerical simulations with the coupled cubic nonlinear Schrödinger (NLS) propagation models with $2 \le N \le 4$ pulse sequences. Thus, we provide the first demonstration of intermediate nonlinear amplitude dynamics in multisequence soliton systems, described by the cubic NLS equation. Our findings are also an important step towards realization of spatio-temporal chaos with multiple periodic sequences of colliding NLS solitons.

nlin.PS↗

arXiv2016

Stabilizing soliton-based multichannel transmission with frequency dependent linear gain-loss

We report several major theoretical steps towards realizing stable long-distance multichannel soliton transmission in Kerr nonlinear waveguide loops. We find that transmission destabilization in a single waveguide is caused by resonant formation of radiative sidebands and investigate the possibility to increase transmission stability by optimization with respect to the Kerr nonlinearity coefficient $γ$. Moreover, we develop a general method for transmission stabilization, based on frequency dependent linear gain-loss in Kerr nonlinear waveguide couplers, and implement it in two-channel and three-channel transmission. We show that the introduction of frequency dependent loss leads to significant enhancement of transmission stability even for non-optimal $γ$ values via decay of radiative sidebands, which takes place as a dynamic phase transition. For waveguide couplers with frequency dependent linear gain-loss, we observe stable oscillations of soliton amplitudes due to decay and regeneration of the radiative sidebands.

nlin.PS↗

arXiv2013

Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction

We study propagation and on-off switching of two colliding soliton sequences in the presence of second-order dispersion, Kerr nonlinearity, linear loss, cubic gain, and quintic loss. Employing a Lotka-Volterra (LV) model for dynamics of soliton amplitudes along with simulations with two perturbed coupled nonlinear Schrödinger (NLS) equations, we show that stable long-distance propagation can be achieved for a wide range of the gain-loss coefficients, including values that are outside of the perturbative regime. Furthermore, we demonstrate robust on-off and off-on switching of one of the sequences by an abrupt change in the ratio of cubic gain and quintic loss coefficients, and extend the results to pulse sequences with periodically alternating phases. Our study significantly strengthens the recently found relation between collision dynamics of sequences of NLS solitons and population dynamics in LV models, and indicates that the relation might be further extended to solitary waves of the cubic-quintic Ginzburg-Landau equation.

nlin.PS↗

arXiv2011

Efficient determination of critical parameters of nonlinear Schr\"{o}dinger equation with point-like potential using generalized polynomial chaos methods

We consider the nonlinear Schr\"{o}dinger equation with a point-like source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, for the given value of the potential strength and the soliton amplitude, there exists a critical velocity of the initial soliton solution, around which the solution is either trapped by or transmitted through the potential. In this paper, we propose an efficient method for finding such a critical velocity by using the generalized polynomial chaos method. For the proposed method, we assume that the soliton velocity is a random variable and expand the solution in the random space using the orthogonal polynomials. The proposed method finds the critical velocity accurately with spectral convergence. Thus the computational complexity is much reduced. Numerical results for the smaller and higher values of the potential strength confirm the spectral convergence of the proposed method.

math.NA↗

arXiv2011

Efficient determination of the critical parameters and the statistical quantities for Klein-Gordon and sine-Gordon equations with a singular potential using generalized polynomial chaos methods

We consider the Klein-Gordon and sine-Gordon type equations with a point-like potential, which describes the wave phenomenon in disordered media with a defect. The singular potential term yields a critical phenomenon--that is, the solution behavior around the critical parameter value bifurcates into two extreme cases. Pinpointing the critical value with arbitrary accuracy is even more challenging. In this work, we adopt the generalized polynomial chaos (gPC) method to determine the critical values and the mean solutions around such values. First, we consider the critical value associated with the strength of the singular potential for the Klein-Gordon equation. We expand the solution in the random variable associated with the parameter. The obtained partial differential equations are solved using the Chebyshev collocation method. Due to the existence of the singularity, the Gibbs phenomenon appears in the solution, yielding a slow convergence of the numerically computed critical value. To deal with the singularity, we adopt the consistent spectral collocation method. The gPC method, along with the consistent Chebyshev method, determines the critical value and the mean solution highly efficiently. We then consider the sine-Gordon equation, for which the critical value is associated with the initial velocity of the kink soliton solution. The critical behavior in this case is that the solution passes through (particle-pass), is trapped by (particle-capture), or is reflected by (particle-reflection) the singular potential if the initial velocity of the soliton solution is greater than, equal to, or less than the critical value, respectively. We use the gPC mean value rather than reconstructing the solution to find the critical parameter. Numerical results show that the critical value can be determined efficiently and accurately by using the proposed method.

math.NA↗

arXiv2011

A multi-domain hybrid method for head-on collision of black holes in particle limit

A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domains only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational costs significantly and also yields the proper power-law decay. Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half maximum and a localized discrete $δ$-function. The discrete $δ$-function was generalized to adopt the Gauss-Lobatto collocation points of the spectral domain. The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized $δ$-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete $δ$-function.

physics.comp-ph↗