Tuesday, February 12, 2013 - 3:05pm
1 hour (actually 50 minutes)
We provide the first construction of exact solitary waves of large amplitude with an arbitrary distribution of vorticity. Small amplitude solutions have been constructed by Hur and later by Groves and Wahlen using a KdV scaling. We use continuation to construct a global connected set of symmetric solitary waves of elevation, whose profiles decrease monotonically on either side of a central crest. This generalizes the classical result of Amick and Toland.