Jianke Yang
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Jianke Yang has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
Sean Nixon
Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA
6 shared publications- Yasuhiro Ohta
Kobe University
5 shared publications Zhigang Chen
Department of Physics and Astronomy San Francisco State University 94132 San Francisco CA USA
4 shared publicationsSean D. Nixon
University of Vermont
3 shared publications- Zhigang Chen
Nankai University
3 shared publications Alexandra Miller
Department of Physics and Astronomy San Francisco State University 94132 San Francisco CA USA
2 shared publications
Latest Publications
- Open Access
Construction of non-PT-symmetric complex potentials with all-real spectra
We review recent work on the generalization of PT symmetry. We show that, in addition to PT-symmetric complex potentials, there are also large classes of non-PT-symmetric complex potentials which also feature all-real spectra. In addition, some classes of these non-PT-symmetric potentials allow phase transitions which do or do not go through exceptional points. These non-PT-symmetric potentials are constructed by a variety of methods, such as the symmetry and supersymmetry methods and the soliton theory. A generalization of PT symmetry in multi-dimensions is also reviewed.
Open AccessConstruction of non-PT-symmetric complex potentials with all-real spectra
We review recent work on the generalization of PT symmetry. We show that, in addition to PT-symmetric complex potentials, there are also large classes of non-PT-symmetric complex potentials which also feature all-real spectra. In addition, some classes of these non-PT-symmetric potentials allow phase transitions which do or do not go through exceptional points. These non-PT-symmetric potentials are constructed by a variety of methods, such as the symmetry and supersymmetry methods and the soliton theory. A generalization of PT symmetry in multi-dimensions is also reviewed.
- 28 November 2018
- Published by Springer Nature
- p. 513-534
Construction of Non- P T $\mathbb {PT}$ -Symmetric Complex Potentials with All-Real Spectra- 28 November 2018
- Published by Springer Nature
- p. 513-534
Construction of Non- P T $\mathbb {PT}$ -Symmetric Complex Potentials with All-Real Spectra- Open Access
General $N$-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
General $N$-solitons in three recently-proposed nonlocal nonlinear Schr\"odinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space-time nonlinear Schr\"odinger equations, which are nonlocal reductions of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. It is shown that general $N$-solitons in these different equations can be derived from the same Riemann-Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann-Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of $N$-solitons in these equations is also explored. In all the three nonlocal equations, a generic feature of their solutions is repeated collapsing. In addition, multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.
Open AccessGeneral $N$-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
General $N$-solitons in three recently-proposed nonlocal nonlinear Schr\"odinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space-time nonlinear Schr\"odinger equations, which are nonlocal reductions of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. It is shown that general $N$-solitons in these different equations can be derived from the same Riemann-Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann-Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of $N$-solitons in these equations is also explored. In all the three nonlocal equations, a generic feature of their solutions is repeated collapsing. In addition, multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.
- Open Access
General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equation
Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the local NLS equation. For instance, the polynomial degrees of their denominators can be not only $n(n+1)$, but also $n(n-1)+1$ and $n^2$, where $n$ is an arbitrary positive integer. Dynamics of these rogue waves is also examined. It is shown that these rogue waves can be bounded for all space and time, or develop collapsing singularities, depending on their types as well as values of their free parameters. In addition, the solution dynamics exhibits rich patterns, most of which have no counterparts in the local NLS equation.Open AccessGeneral rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equation
Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the local NLS equation. For instance, the polynomial degrees of their denominators can be not only $n(n+1)$, but also $n(n-1)+1$ and $n^2$, where $n$ is an arbitrary positive integer. Dynamics of these rogue waves is also examined. It is shown that these rogue waves can be bounded for all space and time, or develop collapsing singularities, depending on their types as well as values of their free parameters. In addition, the solution dynamics exhibits rich patterns, most of which have no counterparts in the local NLS equation. - Open Access
- 4 October 2017
- Published by Optica Publishing Group in Optics Letters
- Vol. 42 (20) , 4067-4070
Classes of non-parity-time-symmetric optical potentials with exceptional-point-free phase transitions
Paraxial linear propagation of light in an optical waveguide with material gain and loss is governed by a Schrödinger equation with a complex potential. In this Letter, new classes of non-parity-time ()-symmetric complex potentials featuring conjugate-pair eigenvalue symmetry are constructed by operator symmetry methods. Due to this eigenvalue symmetry, it is shown that the spectrum of these complex potentials is often all-real. Under parameter tuning in these potentials, a phase transition can also occur, where pairs of complex eigenvalues appear in the spectrum. A distinctive feature of the phase transition here is that the complex eigenvalues may bifurcate out from an interior continuous eigenvalue inside the continuous spectrum; hence, a phase transition takes place without going through an exceptional point. In one spatial dimension, this class of non--symmetric complex potentials is of the form , where is an arbitrary -symmetric complex function. These potentials in two spatial dimensions are also derived. Diffraction patterns in these complex potentials are further examined, and unidirectional propagation behaviors are demonstrated.- 4 October 2017
- Published by Optica Publishing Group in Optics Letters
- Vol. 42 (20) , 4067-4070
Open AccessClasses of non-parity-time-symmetric optical potentials with exceptional-point-free phase transitions
Paraxial linear propagation of light in an optical waveguide with material gain and loss is governed by a Schrödinger equation with a complex potential. In this Letter, new classes of non-parity-time ()-symmetric complex potentials featuring conjugate-pair eigenvalue symmetry are constructed by operator symmetry methods. Due to this eigenvalue symmetry, it is shown that the spectrum of these complex potentials is often all-real. Under parameter tuning in these potentials, a phase transition can also occur, where pairs of complex eigenvalues appear in the spectrum. A distinctive feature of the phase transition here is that the complex eigenvalues may bifurcate out from an interior continuous eigenvalue inside the continuous spectrum; hence, a phase transition takes place without going through an exceptional point. In one spatial dimension, this class of non--symmetric complex potentials is of the form , where is an arbitrary -symmetric complex function. These potentials in two spatial dimensions are also derived. Diffraction patterns in these complex potentials are further examined, and unidirectional propagation behaviors are demonstrated. - Open Access
Transformations between nonlocal and local integrable equations
Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable equations can be converted to local integrable equations through simple variable transformations. Examples include these nonlocal NLS and Davey-Stewartson equations, a nonlocal derivative NLS equation, the reverse space-time complex modified Korteweg-de Vries (CMKdV) equation, and many others. These transformations not only establish immediately the integrability of these nonlocal equations, but also allow us to construct their analytical solutions from solutions of the local equations. These transformations can also be used to derive new nonlocal integrable equations. As applications of these transformations, we use them to derive rogue wave solutions for the partially PT-symmetric Davey-Stewartson equations and the nonlocal derivative NLS equation. In addition, we use them to derive multi-soliton and quasi-periodic solutions in the reverse space-time CMKdV equation. Furthermore, we use them to construct many new nonlocal integrable equations such as nonlocal short pulse equations, nonlocal nonlinear diffusion equations, and nonlocal Sasa-Satsuma equations.
Open AccessTransformations between nonlocal and local integrable equations
Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable equations can be converted to local integrable equations through simple variable transformations. Examples include these nonlocal NLS and Davey-Stewartson equations, a nonlocal derivative NLS equation, the reverse space-time complex modified Korteweg-de Vries (CMKdV) equation, and many others. These transformations not only establish immediately the integrability of these nonlocal equations, but also allow us to construct their analytical solutions from solutions of the local equations. These transformations can also be used to derive new nonlocal integrable equations. As applications of these transformations, we use them to derive rogue wave solutions for the partially PT-symmetric Davey-Stewartson equations and the nonlocal derivative NLS equation. In addition, we use them to derive multi-soliton and quasi-periodic solutions in the reverse space-time CMKdV equation. Furthermore, we use them to construct many new nonlocal integrable equations such as nonlocal short pulse equations, nonlocal nonlinear diffusion equations, and nonlocal Sasa-Satsuma equations.
- 24 March 2017
- Published by IOP Publishing in Journal of Optics
- Vol. 19 (5) , 054004
Nonlinear behaviors in a PDE model for parity-time-symmetric lasers
We propose a phenomenological time-dependent partial differential equation model to investigate the dynamical behaviors of certain parity-time (PT) symmetric lasers during the nonlinear stage of their operations. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken PT symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These theoretical results corroborate the previous experimental results, and reveal the important role the loss plays in maintaining the single-mode operation of PT lasers.
- 24 March 2017
- Published by IOP Publishing in Journal of Optics
- Vol. 19 (5) , 054004
Nonlinear behaviors in a PDE model for parity-time-symmetric lasers
We propose a phenomenological time-dependent partial differential equation model to investigate the dynamical behaviors of certain parity-time (PT) symmetric lasers during the nonlinear stage of their operations. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken PT symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These theoretical results corroborate the previous experimental results, and reveal the important role the loss plays in maintaining the single-mode operation of PT lasers.
- Top Cited PapersOpen Access
- 18 July 2016
- Published by American Physical Society (APS) in Reviews of Modern Physics
- Vol. 88 (3) , 035002
Nonlinear waves in-symmetric systemsRecent progress on nonlinear properties of parity-time ()-symmetric systems is comprehensively reviewed in this article. symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a -symmetric system. The natural inclusion of nonlinearity into these systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of symmetry are pointed out.- 18 July 2016
- Published by American Physical Society (APS) in Reviews of Modern Physics
- Vol. 88 (3) , 035002
Top Cited PapersOpen AccessNonlinear waves in-symmetric systemsRecent progress on nonlinear properties of parity-time ()-symmetric systems is comprehensively reviewed in this article. symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a -symmetric system. The natural inclusion of nonlinearity into these systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of symmetry are pointed out. - Open Access
- 8 June 2016
- Published by Optica Publishing Group in Optics Letters
- Vol. 41 (12) , 2747-2750
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Many classes of non-parity-time ()-symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this Letter, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light’s amplitude evolution. This ODE predicts that a single class of these non--symmetric waveguides supports soliton families and amplitude-oscillating solutions both above and below linear phase transition, in close analogy with -symmetric systems. For the other classes of waveguides, the light’s intensity always amplifies under the effect of nonlinearity, even if the waveguide is below the linear phase transition. These analytical predictions are confirmed by direct computations of the full system.- 8 June 2016
- Published by Optica Publishing Group in Optics Letters
- Vol. 41 (12) , 2747-2750
Open AccessNonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Many classes of non-parity-time ()-symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this Letter, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light’s amplitude evolution. This ODE predicts that a single class of these non--symmetric waveguides supports soliton families and amplitude-oscillating solutions both above and below linear phase transition, in close analogy with -symmetric systems. For the other classes of waveguides, the light’s intensity always amplifies under the effect of nonlinearity, even if the waveguide is below the linear phase transition. These analytical predictions are confirmed by direct computations of the full system. - Open Access
Nonlinear waves in $\cal PT$-symmetric systems
Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\cal PT$-symmetric systems arising from various physical disciplines are presented; nonlinear properties of these systems are thoroughly elucidated; and relevant experimental results are described. In addition, emerging applications of $\cal PT$ symmetry are pointed out.Open AccessNonlinear waves in $\cal PT$-symmetric systems
Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\cal PT$-symmetric systems arising from various physical disciplines are presented; nonlinear properties of these systems are thoroughly elucidated; and relevant experimental results are described. In addition, emerging applications of $\cal PT$ symmetry are pointed out.