Yannan Shen
Assistant professor
Department of Mathematics
California State University, Northridge
18111 Nordhoff St. Northrige, CA, 91330
Office: Santa Susana Hall (SN) 125
Email: yannan.shen@csun.edu
Phone: (818) 6774772
Research interests:
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.
Publications & Preprints for submitted paper:

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

H. Cai, G. Chen, R. Chen and Y. Shen, "Lipschitz metric for the Novikov equation'', Arch. Ration. Mech. Anal. , to appear, (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. (2017) , 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:
Math 481A, Numerical Analysis, Spring 2017.
Math 351, Differential Equations, Spring 2017.
Math 262, Linear Algebra, Fall 2016.
Math 351, Differential Equations, Fall 2016.