Beating effects of vector solitons in Bose-Einstein condensates

Zhao, Li-Chen

doi:10.1103/physreve.97.062201

Cited by 24 publications

(35 citation statements)

References 32 publications

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“…Therefore, the results here predict much more abundant soliton profiles in coupled NLS described systems [53]. Many different types of beating solitons were also demonstrated and more beating patterns are expected [30]. The results here can be used to construct more exotic beating solitons with the help of symmetry properties.…”

Section: Conclusion and Discussionmentioning

confidence: 69%

Solitons in nonlinear systems and eigen-states in quantum wells

Zhao

Yang

2019

Chinese Phys. B

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We study the relations between solitons of nonlinear Schrödinger equation described systems and eigen-states of linear Schrödinger equation with some quantum wells. Many different nondegenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for coupled system with attractive interactions correspond to the identical eigenstates with the ones of coupled systems with repulsive interactions. The energy eigenvalues of them seem to be different, but they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases. On the other hand, we demonstrate soliton solutions in nonlinear systems can be also used to solve the eigen-problems of quantum wells. As an example, we present eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having Parity-Time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as water wave tank, nonlinear fiber, Bose-Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another different way to understand the stability of solitons in nonlinear Schrödinger equation described systems, in contrast to the balance between dispersion and nonlinearity.

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Section: Conclusion and Discussionmentioning

confidence: 69%

Solitons in nonlinear systems and eigen-states in quantum wells

Zhao

Yang

2019

Chinese Phys. B

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“…For simplicity and without losing generality, we investigate the interactions between a NDBSS and one degenerate bright soliton (one NDBSS) by performing thirdfold DT (fourth-fold DT) (see the Appendix A for the detailed solving process). More complicated interaction cases between solitons can be investigated by performing N-fold DT in Appendix A (12). Firstly, we investigate the collision between one NDBSS and a degenerate bright soliton, by performing third-fold DT with spectral parameters λ 1 = a 1 + ib 1 , λ 2 = a 1 + ib 2 , and λ 3 = a 2 + ib 3 .…”

Section: Collision Between Different Non-degenerated Solitonsmentioning

confidence: 99%

Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates

2019

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We investigate non-degenerate bound state solitons systematically in multi-component Bose-Einstein condensates, through developing Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound eigen-states in the self-induced effective quantum wells, in sharp contrast to the bright soliton and dark soliton reported before (which usually correspond to ground state and free eigenstate respectively). We further demonstrate that the bound state solitons with nodes are induced by incoherent interactions between solitons in different components. Moreover, we reveal that the interactions between these bound state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in same component. The bound state solitons can be used to discuss many different physical problems, such as beating dynamics, spin-orbital coupling effects, quantum fluctuations, and even quantum entanglement states.

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“…The dynamics of a single soliton in Fig. 1 exhibits a beating effect [46]. The beating effect comes from the multi-component system with Hermitian symmetry, i.e.…”

Section: Single Soliton Solutionsmentioning

confidence: 97%

Darboux transformation and solitonic solution to the coupled complex short pulse equation

Feng,

Ling

2021

Preprint

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The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather and rogue wave solutions to the CCSP equation. In case of vanishing boundary condition (VBC), we perform the inverse scattering analysis to understand the soliton solution better. Breather and rogue wave solutions are constructed in case of non-vanishing boundary condition (NVBC). Moreover, we conduct a modulational instability (MI) analysis based on the method of squared eigenfunctions, whose result confirms the condition for the existence of rogue wave solution.

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Beating effects of vector solitons in Bose-Einstein condensates

Cited by 24 publications

References 32 publications

Solitons in nonlinear systems and eigen-states in quantum wells

Solitons in nonlinear systems and eigen-states in quantum wells

Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates

Darboux transformation and solitonic solution to the coupled complex short pulse equation

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