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Jianke Yang

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Jianke Yang
NationalityAmerican
OccupationMathematician, professor
Known forResearch on rogue waves, solitons, and nonlinear optics

Jianke Yang is a mathematician and professor of mathematics at the University of Vermont, where his work centers on nonlinear waves, nonlinear optics, and mathematical physics.[1] Over the course of his career, he has published more than two hundred research papers and developed analytical and computational methods used widely in the study of solitons, rogue waves, and photonic lattices.[2] His scholarship, which has been supported by multiple grants from the National Science Foundation, has contributed to the theoretical understanding of nonlinear wave phenomena that arise in optics, fluid dynamics, and related physical systems.[3]

Education

Jianke Yang pursued graduate training in applied mathematics, focusing his early research on nonlinear wave equations and their applications to optical and fluid systems.[1] His doctoral studies established the mathematical foundation that he would later apply to problems in nonlinear optics, soliton theory, and integrable systems, areas that came to define his subsequent academic career.[1] Following the completion of his graduate education, Yang joined the faculty of the University of Vermont, where he has remained for the duration of his academic career.[1]

Career

Jianke Yang has spent his professional career as a faculty member in the Department of Mathematics and Statistics at the University of Vermont.[1] He has held the rank of professor and has taught a range of graduate and undergraduate courses in applied mathematics, differential equations, and mathematical methods for physical sciences.[1]

Throughout his tenure at the University of Vermont, Yang has served as principal investigator on multiple externally funded research projects. The National Science Foundation has supported his work through a series of six grants totaling $975,485.[4] The earliest of these awards, "Effects of Polarization-mode Dispersion on Fiber Communication Systems," was funded on July 9, 1999, for $9,060, and addressed problems relevant to the transmission of optical signals in fiber communication networks.[5]

In subsequent years, Yang's funded research expanded into the analysis of nonlinear light propagation in structured photonic media. The NSF award "Analytical and Numerical Studies of Nonlinear Light Propagation in Two-dimensional Photonic Lattices," funded on August 4, 2009, for $176,494, supported investigations into how nonlinear effects shape the propagation of light through periodic photonic structures.[6] This was followed by "Analytical Studies of Nonlinear Optics in Periodic Media," funded on August 5, 2013, for $198,304, which continued to develop mathematical frameworks for nonlinear optics in periodic environments.[7]

Yang's research program grew further with the award "OP: Mathematical Analysis of Nonlinear Optics in Periodic and Complex Media," funded on June 20, 2016, for $240,000, extending his analytical work to complex, non-Hermitian optical media.[8] His most recent major NSF award, "Mathematical Analysis of Novel Nonlinear Waves in Dissipative Optical Systems," was funded on May 3, 2019, for $291,627, and supported continued investigation into nonlinear wave dynamics in dissipative optical settings.[3] Across these six awards, all administered through the University of Vermont & State Agricultural College, Yang's funded research totals $975,485.[4]

Research

Jianke Yang's research addresses the mathematical theory of nonlinear waves, with particular emphasis on applications in nonlinear optics, integrable systems, and photonic materials.[2] According to citation records, his body of work encompasses 209 publications that have collectively received 9,416 citations, yielding an h-index of 51.[2] This body of scholarship spans theoretical, analytical, and numerical approaches to nonlinear partial differential equations and their solutions.

A recurring theme in Yang's research is the study of rogue waves, transient, large-amplitude wave events that arise in nonlinear systems including optical fibers, fluid surfaces, and other dispersive media. His paper "Rogue wave patterns in the nonlinear Schrödinger equation," published in Physica A: Statistical Mechanics and its Applications in 2021, has been cited more than 100 times and examines the structural patterns formed by rogue wave solutions.[9] Related work, "Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy," published in 2021, has accumulated 62 citations and connects rogue wave structures to a broader class of special polynomial solutions used in integrable systems theory.[10] Yang also contributed to "General rogue waves in the three-wave resonant interaction systems," published in the IMA Journal of Applied Mathematics in 2020 and cited 61 times, as well as "Rogue waves in (2+1)-dimensional three-wave resonant interactions," published in Physica A in 2021 and cited 27 times, both of which extend rogue wave analysis to multi-wave resonant interaction models.[11][12]

Yang's work on the Kadomtsev-Petviashvili I equation, a model describing weakly nonlinear waves in shallow water and other dispersive media, is represented by "Pattern Transformation in Higher-Order Lumps of the Kadomtsev-Petviashvili I Equation," published in the Journal of Nonlinear Science in 2021 and cited 55 times. This paper investigates the transformation of localized lump solutions under varying parameter regimes.[13]

Another strand of Yang's research addresses topological effects in photonic lattices, particularly those modeled on the Su-Schrieffer-Heeger (SSH) framework originally developed for condensed matter systems. His paper "Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices," published in Optics Letters in 2020, has been cited 44 times and analyzes how nonlinear effects interact with topologically protected edge states in photonic systems.[14] Related conference work, "Nonlinear effects on topologically protected linear modes of Su-Schrieffer-Heeger photonic lattices," was presented at the Conference on Lasers and Electro-Optics in 2021.[15]

Yang has also examined soliton solutions in nonlinear Schrödinger equations with complex, non-parity-time-symmetric potentials. His 2021 paper "Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with nonparity-time-symmetric complex potentials," published in Studies in Applied Mathematics, presents analytical techniques for constructing families of soliton solutions in these settings.[16]

In addition to these theoretical contributions, Yang has investigated nonlinear beam propagation in plasmonic nanosuspensions. His 2023 paper "Nonlinear generation of hollow beams in tunable plasmonic nanosuspensions," published in APL Photonics, examines how nonlinear optical effects in engineered nanosuspension media can be used to generate hollow beam profiles.[17] A related conference paper, "Nonlinear hollow beam generation in plasmonic nanosuspensions," was presented at OSA Nonlinear Optics in 2021.[18]

Taken together, Yang's research portfolio demonstrates sustained engagement with the mathematical structures underlying nonlinear wave phenomena, spanning integrable systems theory, rogue wave analysis, topological photonics, and applied nonlinear optics.[2]

Recognition

Jianke Yang's research has been recognized through sustained federal funding, having received six grants from the National Science Foundation over a period spanning from 1999 to 2019, cumulatively totaling $975,485.[4] His publications have collectively accumulated 9,416 citations, and his h-index of 51 reflects the sustained influence of his work within the applied mathematics and nonlinear optics research communities.[2] Several of his papers on rogue waves and integrable systems, including his widely cited 2021 study of rogue wave patterns in the nonlinear Schrödinger equation, rank among the most cited contributions in the specialized literature on rogue wave phenomena.[9]

Publications

  • Yang, J. et al. "Nonlinear generation of hollow beams in tunable plasmonic nanosuspensions." APL Photonics, 2023.[17]
  • Yang, J. et al. "Pattern Transformation in Higher-Order Lumps of the Kadomtsev-Petviashvili I Equation." Journal of Nonlinear Science, 2021.[13]
  • Yang, J. et al. "Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with nonparity-time-symmetric complex potentials." Studies in Applied Mathematics, 2021.[16]
  • Yang, J. et al. "Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy." 2021.[10]
  • Yang, J. et al. "Nonlinear hollow beam generation in plasmonic nanosuspensions." OSA Nonlinear Optics, 2021.[18]
  • Yang, J. et al. "Rogue waves in (2+1)-dimensional three-wave resonant interactions." Physica A: Statistical Mechanics and its Applications, 2021.[12]
  • Yang, J. et al. "Rogue wave patterns in the nonlinear Schrödinger equation." Physica A: Statistical Mechanics and its Applications, 2021.[9]
  • Yang, J. et al. "Nonlinear effects on topologically protected linear modes of Su-Schrieffer-Heeger photonic lattices." Conference on Lasers and Electro-Optics, 2021.[15]
  • Yang, J. et al. "General rogue waves in the three-wave resonant interaction systems." IMA Journal of Applied Mathematics, 2020.[11]
  • Yang, J. et al. "Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices." Optics Letters, 2020.[14]
  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 University of Vermont Department of Mathematics and Statistics faculty page, Jianke Yang.
  2. ↑ 2.0 2.1 2.2 2.3 2.4 Semantic Scholar author profile, Jianke Yang, citation and publication metrics.
  3. ↑ 3.0 3.1 National Science Foundation Award Abstract, "Mathematical Analysis of Novel Nonlinear Waves in Dissipative Optical Systems," Award Number funded May 3, 2019.
  4. ↑ 4.0 4.1 4.2 National Science Foundation award database, summary of grants awarded to Jianke Yang, University of Vermont & State Agricultural College.
  5. ↑ National Science Foundation Award Abstract, "Effects of Polarization-mode Dispersion on Fiber Communication Systems," funded July 9, 1999.
  6. ↑ National Science Foundation Award Abstract, "Analytical and Numerical Studies of Nonlinear Light Propagation in Two-dimensional Photonic Lattices," funded August 4, 2009.
  7. ↑ National Science Foundation Award Abstract, "Analytical Studies of Nonlinear Optics in Periodic Media," funded August 5, 2013.
  8. ↑ National Science Foundation Award Abstract, "OP: Mathematical Analysis of Nonlinear Optics in Periodic and Complex Media," funded June 20, 2016.
  9. ↑ 9.0 9.1 9.2 Yang, J. et al. "Rogue wave patterns in the nonlinear Schrödinger equation." Physica A: Statistical Mechanics and its Applications, 2021.
  10. ↑ 10.0 10.1 Yang, J. et al. "Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy." 2021.
  11. ↑ 11.0 11.1 Yang, J. et al. "General rogue waves in the three-wave resonant interaction systems." IMA Journal of Applied Mathematics, 2020.
  12. ↑ 12.0 12.1 Yang, J. et al. "Rogue waves in (2+1)-dimensional three-wave resonant interactions." Physica A: Statistical Mechanics and its Applications, 2021.
  13. ↑ 13.0 13.1 Yang, J. et al. "Pattern Transformation in Higher-Order Lumps of the Kadomtsev-Petviashvili I Equation." Journal of Nonlinear Science, 2021.
  14. ↑ 14.0 14.1 Yang, J. et al. "Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices." Optics Letters, 2020.
  15. ↑ 15.0 15.1 Yang, J. et al. "Nonlinear effects on topologically protected linear modes of Su-Schrieffer-Heeger photonic lattices." Conference on Lasers and Electro-Optics, 2021.
  16. ↑ 16.0 16.1 Yang, J. et al. "Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with nonparity-time-symmetric complex potentials." Studies in Applied Mathematics, 2021.
  17. ↑ 17.0 17.1 Yang, J. et al. "Nonlinear generation of hollow beams in tunable plasmonic nanosuspensions." APL Photonics, 2023.
  18. ↑ 18.0 18.1 Yang, J. et al. "Nonlinear hollow beam generation in plasmonic nanosuspensions." OSA Nonlinear Optics, 2021.
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