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original research

Focus of Research:

The primary aim of my research is to develop dynamical systems tools in order to explore the qualitative behavior of evolving systems. In particular, I am interested in studying bifurcations of nonlinear waves, and understanding how the structure of these bifurcations impacts the stability of the various resulting waves.  The tools used may be geometric or functional analytic in character, and have application in a wide variety of fields, including optics and neuroscience.


Publications:

  1. Russell K. Jackson, "Multiple pulses in nonlinear optical systems", PhD thesis (2003).
  2. Russell K. Jackson, Christopher K.R.T. Jones and Vadim Zharnitsky, "Dispersion-managed solitons via an averaged variational principle", Physica D 190 (2004), 63-77.
  3. Russell K. Jackson and Michael I. Weinstein, "Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii equation", J. Statist. Phys. 116 (2004), 881-905.
  4. David J. Pinto, Russell K. Jackson and C. Eugene Wayne, "Existence and stability of traveling pulses in a continuous neuronal network",  SIAM J. Appl. Dyn Syst. 4 (2005), 954-984.
  5. Russell K. Jackson, "Pulses in nonlinearly coupled Schrődinger equations I. A homoclinic flip bifurcation",  SIAM J. Appl. Dyn Syst. 5 (2006), 575-597.
  6. Russell K. Jackson and Christopher K. R. T. Jones, "Pulses in nonlinearly coupled Schrődinger equations II. An instability criterion", preprint.