John D. Carter



Research Interests
        I study nonlinear partial differential equations (PDEs), with an emphasis on PDEs that model surface water waves. My work currently focuses on effects such as dispersion, viscosity, surface tension and vorticity. Many of these effects require the use of nonlocal PDEs such as the Whitham, fractional KdV and Dysthe equations. My research interests include stability analysis, fast numerical methods for nonlinear evolution equations and mathematical physics.

If you are a Seattle University student interested in these problems, please contact me regarding research opportunities.

Select Recent Presentations
Publications
  1. C.W. Curtis, J.D. Carter, and H. Kalisch. Deep water particle paths in the presence of currents. Submitted, 2017.   .pdf
  2. J.D. Carter. Bidirectional Whitham equations as models of waves on shallow water. Submitted, 2017.   .pdf
  3. D. Eeltink, A. Lemoine, H. Branger, O. Kimmoun, C. Kharif, J.D. Carter, A. Chabchoub, M. Brunetti, and J. Kasparian. Spectral up- and downshifting of Akhmediev breathers under wind forcing. Physics of Fluids, 29: 107103, 2017.   .pdf
  4. D. Mitsotakis, D. Dutykh, and J.D. Carter. On the nonlinear dynamics of the traveling-wave solutions of the Serre system. Wave Motion, 70: 166-182, 2017.   .pdf
  5. J.D. Carter and A. Govan. Frequency downshift in a viscous fluid. European Journal of Mechanics B: Fluids, 59: 177-185, 2016.   .pdf
  6. J.D. Carter, D. Helliwell, A. Henrich, M. Principe, and J.M. Sloughter. Improving student success in calculus at Seattle University. PRIMUS, 26(2): 105-124, 2016.
  7. N. Sanford, K. Kodama, J.D. Carter, and H. Kalisch. Stability of traveling wave solutions to the Whitham equation. Physics Letters A, 378 : 2100-2107, 2014.   .pdf
  8. J.D. Carter. Plane wave solutions of a dissipative generalization of the vector nonlinear Schrodinger equation. Mathematics and Computers in Simulation, 82: 1038-1046, 2012.   .pdf
  9. J.D. Carter. A Review of Mathematica: A Problem-Centered Approach. SIAM Review, 53: 583-585, 2011.   .pdf
  10. J.D. Carter and R. Cienfuegos. The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations. European Journal of Mechanics B: Fluids, 30: 259-268, 2011.   .pdf
  11. D.M. Henderson, H. Segur and J.D. Carter. Experimental evidence of stable wave patterns on deep water. Journal of Fluid Mechanics, 658, 247-278, 2010.   .pdf
  12. J.D. Carter and C.C. Contreras. Stability of plane-wave solutions of a dissipative generalization of the nonlinear Schrodinger equation. Physica D, 237: 3292-3296, 2008.   .pdf
  13. J.D. Carter. A Review of Maple and Mathematica: A Problem Solving Approach.   .pdf
  14. J.D. Carter. A Review of Mathematica 6. SIAM Review, 50: 149-152, 2008.   .pdf
  15. B. Deconinck, F. Kiyak and J.D. Carter. SpectrUW version 2.0, April 2007.
  16. N. Canney and J.D. Carter. Stability of plane waves on deep water with dissipation. Mathematics and Computers in Simulation, 74: 159-167, 2007.   .pdf
  17. B. Deconinck, F. Kiyak, J.D. Carter and J.N. Kutz. SpectrUW: a laboratory for the numerical exploration of spectra of linear operators.Mathematics and Computers in Simulation, 74: 370-378, 2007.   .pdf
  18. J.D. Carter and B. Deconinck. Instabilities of one-dimensional trivial-phase solutions of the two-dimensional cubic nonlinear Schrodinger equation. Physica D, 214: 42-54, 2006.   .pdf
  19. B. Deconinck, D.E. Pelinovsky and J.D. Carter. Transverse instabilities of deep-water solitary waves. Proceedings of the Royal Society A, 462: 2039-2061, 2006.   .pdf
  20. R.J. Thelwell, J.D. Carter and B. Deconinck. Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation. Journal of Physics A: Mathematical and General, 39: 73-84, 2006.   .pdf
  21. H. Segur, D. Henderson, J.D. Carter, J. Hammack, C. Li, D. Pheiff and K. Socha. Stabilizing the Benjamin-Feir instability. Journal of Fluid Mechanics, 539: 229-271, 2005.   .pdf
  22. J.D. Carter. A Review of Mathematica 5.0. SIAM Review, 46: 564-568, 2004.   .pdf
  23. J.D. Carter and H. Segur. Instabilities in the two-dimensional cubic nonlinear Schrodinger equation. Physical Review E, 68: 045601, 2003.   .pdf
  24. J.D. Carter (Ph.D. thesis). Stability and existence of traveling-wave solutions of the two-dimensional nonlinear Schrodinger equation and its higher-order generalizations. University of Colorado at Boulder, 2001.   .pdf
Curriculum Vitae
Feb 11 PDE Data
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