Yannan Shen

Associate professor

Department of Mathematics

The University of Kansas

1460 Jayhawk Blvd., Lawrence, KS 66045

Office: 509 Snow Hall

Email: yshen@ku.edu

CV

Research

Applied mathematics, models from physics and engineering, such as optical systems, metamaterials, plasmas and Bose-Einstein condensates. These physical models are described by differential equations such as the nonlinear Schrodinger equation, complex Ginzburg Landau equation, short pulse equation. My research mainly involves existence, stability and dynamics of solitary wave solutions. Methods employed include asymptotics, variational approximations, rigorous analysis, numerical analysis, as well as scientific computing.

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The research is partially supported by NSF DMS-206218 (2022-2025)

Publications

  1. G. Chen, Y. Shen, S. Zhu, "Existence and regularity for global solutions including breaking waves from Camassa-Holm and Novikov equations to lambda-family equations", Quart. Appl. Math. (2023)

  2. Y. Du, M. Lu, Y. Shen, "The 3D Boussinesq system with partial viscosity and large data in thin domain'', submitted

  3. H. Cai, G. Chen, Y. Shen, "A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation'', J. Diff. Eq., 356, 289 (2023).

  4. H. Cai, G. Chen, Y. Du, Y. Shen, "Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle'', J. Math. Phys 63, 021508 (2022)

  5. R. Parker, Y. Shen, A. Aceves, J. Zweck, “Spatiotemporal dynamics in a twisted, circular waveguide array”, Stud. Appl. Math., 149, 537 (2022).

  6. J. Zweck, Y. Chen, M. J. Goeckner and Y. Shen, "Spectral computation of low probability tails for the homogeneous Boltzmann equation", Applied Numerical Mathematics, 162 , 301-317 (2021).

  7. H. Cai, G. Chen, R. Chen and Y. Shen, "Lipschitz metric for the Novikov equation'', Arch. Ration. Mech. Anal., 229,1091 (2018).

  8. Y. Shen, P.G. Kevrekidis, G.P. Veldes, D.J. Frantzeskakis, D. DiMarzio, X. Lan, and V. Radisic "From Solitons to Rogue Waves in Nonlinear Left-Handed Metamaterials'', Phys. Rev. E. , 95, 032223 (2017).

  9. H. Cai, G. Chen, Y. Shen, "Lipschitz metric for conservative solutions of the two-component Camassa-Holm system'', Z. Angew. Math. Phys. , 68, 5 (2017).

  10. C. Castro-Castro, Y. Shen, G. Srinivasan, A. Aceves and P.G. Kevrekidis, "Light dynamics in nonlinear trimers and twisted multicore fibers", J. Nonlinear Optic. Phys. Mat. , 25 , 1650042 (2016) .

  11. H. Cai, G. Chen, Y. Shen, Z. Tan, "Generic Regularity and Lipschitz Metric for the Hunter-Saxton type equations'', J. Diff. Eq. , 262, 1023 (2017).

  12. Y. Shen, P.G. Kevrekidis, G. Srinivasan, and A. Aceves, "Existence, Stability and Dynamics of Discrete Solitary Waves in a Binary Waveguide Array", J. Phys. A: Math. Theor., 49, 295205 (2016).

  13. Y. Shen, John Zweck, Shaokang Wang, and Curtis R. Menyuk, "Spectra of Short Pulse Solutions of the Cubic-Quintic Complex Ginzburg Landau Equation near Zero Dispersion", Studies in Applied Mathematics, 137, 238(2016).

  14. G. Chen, Y. Shen, ''Existence and regularity of solutions in nonlinear wave equations'', Disc. Contin. Dyn. Syst., Ser. A , 35, 3327 (2015).

  15. Y. Shen, P. G. Kevrekidis, S. Sen, A. Hoffman, "Characterizing traveling-wave collisions in granular chains starting from integrable limits: The case of the Korteweg-de Vries equation and the Toda lattice", Phys. Rev. E, 90 (2), 022905 (2014).

  16. Y. Shen, T. P. Horikis, P. G. Kevrekidis, D. J. Frantzeskakis, "Traveling waves of the regularized short pulse equation'', J. Phys. A: Math. Theor., 47, 315204 (2014).

  17. Y. Shen, P. G. Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis, "Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction", Phys. Rev. A, 86, 033616 (2012).

  18. Y. Shen, N. Whitaker, P. G. Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis, "Ultrashort pulses and short-pulse equations in (2+1)-dimensions", Phys. Rev. A, 86, 023841 (2012).

  19. Y. Shen, P. G. Kevrekidis, N. Whitaker, Boris A. Malomed, "Spatial solitons under competing linear and nonlinear diffractions", Phys. Rev. E, 85, 026606 (2012).

  20. L. Q. English, S. G. Wheeler, Y. Shen, G. P. Veldes, N. Whitaker, P. G. Kevrekidis, D. J. Frantzeskakis, "Backwards-wave propagation and discrete solitons in a left-handed electrical lattice", Phys. Lett. A, 375, 1242 (2011).

  21. A. Stefanov, Y. Shen, P. G. Kevrekidis, "Well-posedness and small data scattering for the generalized Ostrovsky equation", J. Diff. Eq., 249, 2600 (2010).

  22. Y. Shen, F. Williams, N. Whitaker, P. G. Kevrekidis, A. Saxena and D. J. Frantzeskakis, "On some single-hump solutions of the short-pulse equation and their periodic generalizations'', Phys. Lett. A , 374, 2964 (2010).

  23. N. L. Tsitsas, T. P. Horikis, Y. Shen, P. G. Kevrekidis, N. Whitaker, D. J. Frantzeskakis, "Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials", Phys. Lett. A, 374, 1384 (2010) .

Teaching