Yannan Shen

The University of Texas at Dallas
Department of Mathematical Sciences, FO 35
800 West Campbell Road,
Richardson, TX 75080

Office: FO 2.106

Email: yxs135630@utdallas.edu

CV

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Teaching: Math2417 Office hour MWF 1:30-2:00pm

Research Interests:

My research is in the field of applied mathematics, focuses on mathematical physics models of metamaterials, optical systems and Bose-Einstein condensates, where the physical settings are modeled by nonlinear partial differential equations. My research mainly revolves around the derivation of equations, their Hamiltonian structure, existence, stability and dynamics of the solitary wave solutions. Methods employed include asymptotics, variational approximations, rigorous analysis, numerical analysis, as well as scientific computing.

Publications:

  1. Existence and regularity of solutions in nonlinear wave equations, G. Chen, Y. Shen, to appear in Discrete Contin. Dyn. Syst., Series A PDF
  2. Characterizing traveling-wave collisions in granular chains starting from integrable limits: The case of the Korteweg-de Vries equation and the Toda lattic, Y Shen, PG Kevrekidis, S Sen, A Hoffman, Physical Review E 90 (2), 022905 (2014). PDF
  3. Traveling waves of the regularized short pulse equation, Y. Shen, T. P. Horikis, P. G. Kevrekidis, D. J. Frantzeskakis, J. Phys. A: Math. Theor. 47 (2014), 31524. PDF
  4. Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction, Y. Shen, P. G. Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis, Phys. Rev. A. 86, 033616, (2012). PDF
  5. Ultrashort pulses and short-pulse equations in (2+1)-dimensions, Y. Shen, N. Whitaker, P. G. Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis, Phys. Rev. A 86, 023841, (2012). PDF
  6. Spatial solitons under competing linear and nonlinear diffractions, Y. Shen, P. G. Kevrekidis, N. Whitaker, Boris A. Malomed, Phys. Rev. E 85, 026606, (2012). PDF
  7. Backwards-wave propagation and discrete solitons in a left-handed electrical lattice, L. Q. English, S. G. Wheeler, Y. Shen, G. P. Veldes, N. Whitaker, P. G. Kevrekidis, D. J. Frantzeskakis, Phys. Lett. A 375 (2011), 1242.PDF
  8. Well-posedness and small data scattering for the generalized Ostrovsky equation, A. Stefanov, Y. Shen, P. G. Kevrekidis, J. Diff. Eq. , 249 (2010), 2600. PDF
  9. On some single-hump solutions of the short-pulse equation and their periodic generalizations, Y. Shen, F. Williams, N. Whitaker, P. G. Kevrekidis, A. Saxena and D. J. Frantzeskakis, Phys. Lett. A 374 (2010), 2964. PDF
  10. Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials, N. L. Tsitsas, T. P. Horikis, Y. Shen, P. G. Kevrekidis, N. Whitaker, D. J. Frantzeskakis, Phys. Lett. A 374 (2010) 1384. PDF
  11. Fairing Algorithm of Quintic Parametric Splines with Using Energy Optimization, Yuanjun Wang, Yannan Shen, CSIAM Geometric Design & Computing (2005).
  12. A Research Report of the Investment Environment in Qingdao, Dissertation, Ocean University of China (2002).