Complex solitons in Bose–Einstein condensates with two- and three-body interactions

We illustrate the analytical control of the Akhmediev breather frequency in BoseEinstein condensate in a time varying parabolic trap. This is achieved by varying Feshbach managed scattering length R(t) within the integrability framework. Recognizing the mathematical relation between R(t) and parabolic trap with the linear Schrödinger equation, we use isospectral Hamiltonian approach, which leads to a one parameter family of nonlinearity control functions, directly affecting the characteristic scales of the solution space, for the same trapping potential. The chirp equation and the trap equation being same, the phase of the wave for the obtained class of nonlinearity function remains identical. For explicating the general applications of the present approach, we exhibit breather frequency control in a number of cases, with asymptotically vanishing nonlinearity, for expulsive parabolic trap. Interestingly, the same procedure is found to provide a free parameter, which controls the Rogue wave amplitude.

show abstract

“…The present work can be extended for the three body interaction case, where complex power law solitons exist. 33 …”

Section: Resultsmentioning

confidence: 99%

Combined control of Akhmediev breather frequency and rogue wave amplitude: An analytical approach

Loomba

Gupta

Kumar

et al. 2015

J. Nonlinear Optic. Phys. Mat.

View full text Add to dashboard Cite

show abstract

“…In particular, linear couplings between parallel photonic nanowires [30][31][32][33] may display strong dispersion, which can consequently generate especially pronounced MI effects. The associated spatiotemporal solitary pulses and other related soliton phenomena [34] suggest fruitful directions of future research. and C 1 = 0 ps m -1 .…”

Section: Discussionmentioning

confidence: 98%

Modulation instabilities in birefringent two-core optical fibres

Chiang

Malomed

et al. 2012

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

Previous studies of the modulation instability (MI) of continuous waves (CWs) in a two-core fibre (TCF) did not consider effects caused by co-propagation of the two polarized modes in a TCF that possesses birefringence, such as cross-phase modulation (XPM), polarization-mode dispersion (PMD) and polarization-dependent coupling (PDC) between the cores. This paper reports an analysis of these effects on the MI by considering a linear-birefringence TCF and a circular-birefringence TCF, which feature different XPM coefficients. The analysis focuses on the MI of the asymmetric CW states in the TCFs, which have no counterparts in single-core fibres. We find that the asymmetric CW state exists when its total power exceeds a threshold (minimum) value, which is sensitive to the value of the XPM coefficient. We consider, in particular, a class of asymmetric CW states that admit analytical solutions. In the anomalous dispersion regime, without taking the PMD and PDC into account, the MI gain spectra of the birefringent TCF, if scaled by the threshold power, are almost identical to those of the zero-birefringence TCF. However, in the normal dispersion regime, the power-scaled MI gain spectra of the birefringent TCFs are distinctly different from their zero-birefringence counterparts, and the difference is particularly significant for the circular-birefringence TCF, which takes a larger XPM coefficient. On the other hand, the PMD and PDC only exert weak effects on the MI gain spectra. We also simulate the nonlinear evolution of the MI of the CW inputs in the TCFs and obtain good agreement with the analytical solutions.

show abstract

Section: Discussionmentioning

confidence: 98%

Modulation Instabilities in Birefringent Two-core Optical Fibers

Chiang

Malomed

et al. 2012

Asia Communications and Photonics Conference

View full text Add to dashboard Cite

Previous studies of the modulation instability (MI) of continuous waves (CWs) in a two-core fiber (TCF) did not consider effects caused by co-propagation of the two polarized modes in a TCF that possesses birefringence, such as cross-phase modulation (XPM), polarization-mode dispersion (PMD), and polarization-dependent coupling (PDC) between the cores. This paper reports an analysis of these effects on the MI by considering a linear-birefringence TCF and a circular-birefringence TCF, which feature different XPM coefficients. The analysis focuses on the MI of the asymmetric CW states in the TCFs, which have no counterparts in single-core fibers. We find that, the asymmetric CW state exists when its total power exceeds a threshold (minimum) value, which is sensitive to the value of the XPM coefficient. We consider, in particular, a class of asymmetric CW states that admit analytical solutions. In the anomalous dispersion regime, without taking the PMD and PDC into account, the MI gain spectra of the birefringent TCF, if scaled by the threshold power, are almost identical to those of the zero-birefringence TCF. However, in the normal dispersion regime, the power-scaled MI gain spectra of the birefringent TCFs are distinctly different from their zero-birefringence counterparts, and the difference is particularly significant for the circular-birefringence TCF, which takes a larger XPM coefficient. On the other hand, the PMD and PDC only exert weak effects on the MI gain spectra. We also simulate the nonlinear evolution of the MI of the CW inputs in the TCFs and obtain a good agreement with the analytical solutions.

show abstract

Complex solitons in Bose–Einstein condensates with two- and three-body interactions

Cited by 38 publications

References 65 publications

Combined control of Akhmediev breather frequency and rogue wave amplitude: An analytical approach

Combined control of Akhmediev breather frequency and rogue wave amplitude: An analytical approach

Modulation instabilities in birefringent two-core optical fibres

Modulation Instabilities in Birefringent Two-core Optical Fibers

Contact Info

Product

Resources

About