On the Stability of Periodic Solutions of Nonlinear Dispersive Equations

187 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.Finally, we show how our results extend to other classes of dispersive equations. In particular, we derive modulational and finite-wavelength instability indices for the generalized Benjamin-Bona-Mahony (gBBM) equation, as well as the generalized Camassa-Holm equation. Moreover, we prove a transverse instability result for the gBBM equation analogous to that for the gKdV.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD