Research
Applied mathematics, models from physics and engineering, such as optical systems, metamaterials,
plasmas and BoseEinstein 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.
The research is partially supported by NSF DMS206218 (20222025)
Publications

G. Chen, Y. Shen, S. Zhu, "Existence and regularity for global solutions including breaking waves from CamassaHolm and Novikov equations to lambdafamily equations", Quart. Appl. Math. (2023)

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

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

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

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

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 , 301317 (2021).

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

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 LeftHanded Metamaterials'', Phys. Rev. E. , 95, 032223 (2017).

H. Cai, G. Chen, Y. Shen, "Lipschitz metric for conservative solutions of the twocomponent CamassaHolm system'', Z. Angew. Math. Phys. , 68, 5 (2017).

C. CastroCastro, 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) .

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

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).

Y. Shen, John Zweck, Shaokang Wang, and Curtis R. Menyuk, "Spectra of Short Pulse Solutions of the CubicQuintic Complex Ginzburg Landau Equation near Zero Dispersion", Studies in Applied Mathematics, 137, 238(2016).
 G. Chen, Y. Shen,
''Existence and regularity of solutions in nonlinear wave equations'',
Disc. Contin. Dyn. Syst., Ser. A , 35, 3327 (2015).
 Y. Shen, P. G. Kevrekidis, S. Sen, A. Hoffman, "Characterizing travelingwave collisions in granular chains starting from integrable limits: The case of the Kortewegde Vries equation and the Toda lattice", Phys. Rev. E, 90 (2), 022905 (2014).
 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).

Y. Shen, P. G. Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis, "Finitetemperature dynamics of matterwave dark solitons in linear and periodic potentials: an example of an antidamped Josephson junction", Phys. Rev. A, 86, 033616 (2012).
 Y. Shen, N. Whitaker, P. G. Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis, "Ultrashort pulses and shortpulse equations in (2+1)dimensions", Phys. Rev. A, 86, 023841 (2012).
 Y. Shen, P. G. Kevrekidis, N. Whitaker, Boris A. Malomed, "Spatial solitons under competing linear and nonlinear diffractions", Phys. Rev. E, 85, 026606 (2012).
 L. Q. English, S. G. Wheeler, Y. Shen, G. P. Veldes, N. Whitaker, P. G. Kevrekidis, D. J. Frantzeskakis, "Backwardswave propagation and discrete solitons in a lefthanded electrical lattice", Phys. Lett. A, 375, 1242 (2011).
 A. Stefanov, Y. Shen, P. G. Kevrekidis, "Wellposedness and small data scattering for the generalized Ostrovsky equation", J. Diff. Eq., 249, 2600 (2010).
 Y. Shen, F. Williams, N. Whitaker, P. G. Kevrekidis, A. Saxena and D. J. Frantzeskakis, "On some singlehump solutions of the shortpulse equation and their periodic generalizations'', Phys. Lett. A , 374, 2964 (2010).
 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
 Spring 2024, Math 221 Applied Differential Equations, Honors
 Spring 2024, Math 500 Intermediate Analysis
 Fall 2023, Math 647 Applied Partial Differential Equations
 Spring 2023, Math 783 Numerical PDE
 Spring 2023, Math 500 Intermediate Analysis
 Fall 2022, Math765 Mathematical Analysis I
 Spring 2022, Math 290 Elementary Linear Algebra (two sections)
 Fall 2021, Math 950 Partial Differential Equations
 Spring 2021, Math 500 Intermediate Analysis
 Fall 2020, Math 647 Applied Partial Differential Equations
 Spring 2020, Math 500 Intermediate Analysis