My research primarily consists of using analytical, asymptotic, and numerical tools to investigate qualitative features of nonlinear dispersive wave phenomena, including dispersive shock waves and solitary waves. My current work is investigating these structures in the context of both shallow water and magnetic surface spin waves. For more information regarding current and published work, please see the manuscripts listed below. Feel free to contact me if you have any questions or suggestions.
PS and M. A. Hoefer. Shock waves in dispersive hydrodynamics with non-convex dispersion. SIAM J. Appl. Math 77, 26–50 (2017) (preprint)
Janantha, PA Praveen, PS, Mark A. Hoefer, and Mingzhong Wu. Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films. PRL 119, no. 2 (2017): 024101. (preprint)
PS, M. A. Hoefer, and G. A El. Hydrodynamic Optical Soliton Tunneling. Phys. Rev. E. 97 (2018): 032218. (preprint)
M. A. Hofer, N. F. Smyth, and PS. Modulation theory solution for nonlinearly resonant, fifth order Korteweg-de Vries non-classical traveling dispersive shock waves. (submitted)
PS, M. A. Hofer, E. Iacocca. Nonlocal dipole effects on spin density waves. (preprint)
K. L. Oliveras, PS, and V. Vasan. Stability of periodic traveling waves with a constant vorticity. (in preparation)