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 bathymetry, 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.

Publications

- D.M. Henderson, M.E. Catalano, and J.D. Carter. On the variation of of bi-periodic waves in the transverse direction.
*Submitted*, 2021. .pdf - H. Potgieter, J.D. Carter, and D.M. Henderson. Modeling the second harmonic in surface water waves using generalizations of NLS.
*Submitted*, 2021. .pdf - C.R. Zaug and J.D. Carter. Dissipative models of swell propagation across the Pacific.
*In Press*, 2021. .pdf - J.D. Carter, E. Dinvay, and H. Kalisch. Fully dispersive Boussinesq models with uneven bathymetry.
*Journal of Engineering Mathematics*,**127**: 10, 2021. .pdf - J.D. Carter, C.W. Curtis, and H. Kalisch. Particle trajectories in nonlinear Schrodinger models.
*Water Waves*,**2**: 31-57, 2020. .pdf - C. Kharif, M. Abid, J.D. Carter, and H. Kalisch, Stability of periodic progressive gravity wave solutions of the Whitham equation in the presence of vorticity,
*Physics Letters A*,**384**(2), 126060, 2020. .pdf - J.D. Carter and M. Rozman, Stability of periodic, traveling-wave solutions to the capillary-Whitham equation.
*Fluids*,**4**(1): 58, 2019. .pdf - J.D. Carter, D. Henderson, and I. Butterfield. A comparison of frequency downshift
models of wave trains on deep water.
*Physics of Fluids*,**31**: 013103, 2019. .pdf - C.W. Curtis, J.D. Carter, and H. Kalisch. Deep water
particle paths in the presence of currents.
*Journal of Fluid Mechanics*,**855**: 322-350, 2018. .pdf - J.D. Carter. Bidirectional Whitham equations as models
of waves on shallow water.
*Wave Motion*,**82**: 51-61, 2018. .pdf - 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 *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*J.D. Carter and A. Govan. Frequency downshift in a viscous fluid.**European Journal of Mechanics B: Fluids*,**59**: 177-185, 2016. .pdf*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.*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*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*J.D. Carter. A Review of**Mathematica: A Problem-Centered Approach.**SIAM Review*,**53**: 583-585, 2011. .pdf*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*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*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*J.D. Carter. A Review of**Maple and Mathematica: A Problem Solving Approach*. .pdf- J.D. Carter. A Review of
*Mathematica 6*.*SIAM Review*,**50**: 149-152, 2008. .pdf - B. Deconinck, F. Kiyak and J.D. Carter. SpectrUW version 2.0, April 2007.
- 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 - 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 - 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 - 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 - 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 - 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 - J.D. Carter. A Review of
*Mathematica 5.0*.*SIAM Review*,**46**: 564-568, 2004. .pdf - J.D. Carter and H. Segur. Instabilities in the two-dimensional
cubic nonlinear Schrodinger equation.
*Physical Review E*,**68**: 045601, 2003. .pdf - 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

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