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Roy H. Goodman
Chair, Mathematical Sciences Club & Pi Mu EpsilonAssistant Professor
Phone: 973-642-4261
Email: goodman@njit.edu
Dept: Mathematical Sciences
Room: 624 * Cullimore Hall
Website: http://m.njit.edu/goodman
Education
PhD, Mathematical Sciences, Courant Institute, New York University
BS, Mathematics, University of Michigan
Areas of Research
Roy Goodman's research focuses, broadly, on nonlinear wave phenomena. The tools he uses consist mainly of asymptotic methods, dynamical systems analysis, and numerical simulation. Physical applications he has studied include storm propagation in the atmosphere at middle latitudes and the interaction of light pulses in telecommunications optical fibers. Recently, he has been investigating the interaction of nonlinear waves with localized changes to the media through which they propagate. This includes the enticing possibility of "light trapping" at specified locations in optical fibers, as well as more abstract studies of classical nonlinear wave equations.
Selected Publications
R. H. Goodman and R. Haberman, 2005, "Kink-antikink collisions in the phi-four equation: The n-bounce resonance and the separatrix map," submitted to SIAM J. App. Dyn. Sys. , pp.
R. H. Goodman and R. Haberman, 2005, "Vector soliton interactions in birefringent optical fibers," Phys. Rev. E 71, pp. 056605
Goodman, R.H. and P. J. Holmes and M. I. Weinstein, 2004, "Strong NLS soliton--defect interactions," Phys. D 192, pp. 215--248
R. H. Goodman and R. Haberman, 2004, "Interaction of sine-Gordon kinks with defects: The two-bounce resonance," Phys. D. 195, pp. 303--323
R. H. Goodman, P. J. Holmes, and M. I. Weinstein, 2002, "Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model," Phys. D 161, pp. 21--44
R. H. Goodman, R. E. Slusher, and M. I. Weinstein, 2002, "Stopping Light on a Defect," J. Opt. Soc. Am. B 19, pp. 1635--1632
R. H. Goodman, A. J. Majda and D. W. McLaughlin, 200, "Modulations in the leading edges of midlatitude storm tracks," SIAM J. Appl. Math. 62, pp. 746--776
R. H. Goodman,M. I. Weinstein, and P. J. Holmes, 200, "Nonlinear propagation of light in one-dimensional periodic structures," J. Nonlinear Science 11, pp. 123--168
R. H. Goodman, D. S. Graff, L. M. Sander, P. Leroux-Hugon, and E. Clement, 1995, "Trigger Waves in a Model for Catalysis," Phys. Rev. E 52, pp. 5904--5909