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Solitons in nonlinear systems and eigen-states in quantum wells

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Chinese Physics B 2019年第1期28卷 257-266页

作者： Li-Chen Zhao zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi’an 710069China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi’an 710069China Institute of Modern Physics Northwest UniversityXi’an 710069China

We study the relations between solitons of nonlinear Schro¨dinger equation and eigen-states of linear Schro¨dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for the coupled system with attractive interactions correspond to the identical eigen-states with the ones of the coupled systems with repulsive interactions. Although their energy eigenvalues seem to be different, 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 ***, we demonstrate that soliton solutions in nonlinear systems can also be used to solve the eigen-problems of quantum wells. As an example, we present the 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 a water wave tank, nonlinear fiber, Bose–Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another way to understand the stability of solitons in nonlinear Schro¨dinger equation described systems, in contrast to the balance between dispersion and nonlinearity.

关键词： non-degenerated soliton eigen-states quantum well nonlinear Schrodinger equation

Breather-induced quantised superfluid vortex filaments and their characterisation

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Communications in Theoretical Physics 2020年第7期72卷 132-140页

作者： Hao Li Chong Liu Wei Zhao zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi’an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710127China NSFC-SPTP Peng Huanwu Center for Fundamental Theory Xi’an 710127China Institute of Modern Physics Northwest UniversityXi'an 710127China Institute of Photonics and Photon-technology Northwest UniversityXi'an 710127China State Key Laboratory of Photoelectric Technology and Functional Materials Xi'an 710127China

We study and characterise the breather-induced quantised superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised *** vortex filaments,emerging from an otherwise perturbed helical vortex,exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the *** loop induced by the Kuznetsov-Ma breather emerges periodically as time increases,while the loop structure triggered by the superregular breather—the loop pair—exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of the super-regular *** particular,we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity—the integral of the relative quadratic curvature—which corresponds to the effective energy of *** the nature of nonlinearity,it is demonstrated that this physical quantity shows a linear correlation with the loop *** results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.

关键词： vortex filament loop structure local induction approximation Kuznetsov-Ma breather super-regular breather

Reverse Rotation of Ring-Shaped Perturbation on Homogeneous Bose–Einstein Condensates

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Chinese Physics Letters 2021年第9期38卷 11-17页

作者： Peng Gao Zeyu Wu zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi’an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi’an 710127China Department of Physics and Astronomy University College LondonLondon WC1E 6BTUK Peng Huanwu Center for Fundamental Theory Xi’an 710127China Institute of modern Physics Northwest UniversityXi’an 710127China

We numerically study the dynamics of rotating ring-shaped perturbation on two-dimensional homogeneous Bose–Einstein condensates,where a new ring-shaped structure with reverse rotation *** reversely rotating mode is directly caused by the existence of the plane wave(namely the homogeneous background).By the modified linear stability analysis method,we quantitatively predict the influence of the background’s density on perturbation dynamics,including the velocity,amplitude,and frequency of the two *** construct an approximative solution to describe the short-lived dynamics of initial perturbation,which agrees well with our numerical ***,after the two rings separate,the transfer of atom number between them becomes linear,and the rate of transfer is impacted by the radial momentum of initial perturbation.

关键词： perturbation perturbation Einstein

Quantized Superfluid Vortex Filaments Induced by the Axial Flow Effect

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Chinese Physics Letters 2020年第3期37卷 5-8页

作者： Hao Li Chong Liu zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi'an 710127 Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710127 NSFC-SPTP Peng Huanwu Center for Fundamental Theory Xi'an 710127 Institute of Modern Physics Northwest UniversityXi'an 710127

We report the quantized superfluid vortex filaments induced by the axial flow effect,which exhibit intriguing loop structures on helical *** new vortex filaments correspond to a series of soliton excitations including the multipeak soliton,W-shaped soliton,and anti-dark soliton,which have no analogue when the axial flow effect is *** particular,we show that the vortex filaments induced by the multipeak soliton and W-shaped soliton arise from the dual action of bending and twisting of the vortex,while the vortex filament induced by the anti-dark soliton is caused only by the bending action,which is consistent with the case of the standard bright *** results will deepen our understanding of breather-induced vortex filaments and will be helpful for controllable ring-like excitations on vortices.

关键词： soliton vortex bending

Merging and splitting dynamics between two bright solitons in dipolar Bose-Einstein condensates

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Chinese Physics B 2021年第12期30卷 233-236页

作者： Xin Li Peng Gao zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi’an 710069China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi’an 710069China Peng Huanwu Center for Fundamental Theory Xi’an 710127China Institute of Modern Physics Northwest UniversityXi’an 710069China

We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose-Einstein *** different dipolar strengths,the two bright solitons can merge into a breathing wave,and then split or propagate constantly after several oscillating *** quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting,and analyze their formation mechanism by the system's energy ***,the change of initial phase difference brings distinct effects on the soliton *** results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons.

关键词： bright soliton Bose-Einstein condensate dipolar soliton

Boundedness of Convolution-Type Operators on Endpoint Triebel-Lizorkin Spaces

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Journal of Mathematical Research and Exposition 2011年第5期31卷 863-873页

作者： zhan ying yang School of Mathematics and statistics South-Central University for Nationalities Hubei 430074 P. R. China

This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the author establishes the boundedness on certain endpoint Triebel-Lizorkin spaces F˙10 ,q（2 q ≤ ∞） under a very weak pointwise regularity condition.

关键词： convolution-type Calderón-Zygmund operators endpoint Triebel-Lizorkin spaces wavelets molecular decomposition.

Vector kink-dark complex solitons in a three-component Bose–Einstein condensate

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Communications in Theoretical Physics 2021年第5期73卷 85-91页

作者： Yan Li Yan-Hong Qin Li-Chen Zhao zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi'an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi’an 710127 China Peng Huanwu Center for Fundamental Theory Xi’an 710127China

We investigate kink-dark complex solitons(KDCSs)in a three-component Bose–Einstein condensate(BEC)with repulsive interactions and pair-transition(PT)*** profiles critically depend on the phase differences between dark solitons excitation *** report a type of kink-dark soliton profile which shows a droplet-bubble-droplet with a density dip,in sharp contrast to previously studied *** interaction between two KDCSs is further *** demonstrates some striking particle transition behaviours during their collision processes,while soliton profiles survive after the ***,we exhibit the state transition dynamics between a kink soliton and a dark *** results suggest that PT effects can induce more abundant complex solitons dynamics in multi-component BEC.

关键词： kink-dark complex solitons pair-transition effects three-component Bose–Einstein condensate

Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction

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Chinese Physics Letters 2020年第4期37卷 9-13页

作者： Yu-Han Wu Chong Liu zhan-ying yang Wen-Li yang School of Physics Northwest UniversityXi'an 710127 Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710127 NSFC-SPTP Peng Huanwu Center for Fundamental Theory Xi'an 710127 Institute of Modern Physics Northwest UniversityXi7an 710127

We study the properties of breather interactions in nonlinear Kerr media with self-steepening and space-time correction and with either self-focusing or self-defocusing nonlinearity,and present a new family of exact breather solutions via the Darboux transformation with a special-designed quadratic spectral *** contrast to the previous results of the nonlinear Schrodinger equation(NLSE)hierarchy,we show that the relative phase of colliding breathers has a significant effect on the collision *** particular,only the out-of-phase interactions can generate small amplitude waves at the collision center,which are analogous to the NLSE superregular *** results will deepen our understanding of the properties of breather interactions and they will offer the possibility of experimental observations of super-regular breather dynamics in systems with self-steepening and space-time correction.

关键词： parameter. collision nonlinear

Localized Optical Waves in Defocusing Regime of Negative-Index Materials

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Chinese Physics Letters 2017年第10期34卷 8-12页

作者： Wen-Hao Xu zhan-ying yang Chong Liu Wen-Li yang School of Physics Northwest University Xi'an 710069 Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710069 Institute of Modern Physics Northwest University Xi'an 710069

We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intrigu- ing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is estab- lished in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.

关键词： In Localized Optical Waves in Defocusing Regime of Negative-Index Materials