Lower Bounds for Non-Trivial Traveling Wave Solutions of Equations of   KdV Type
  We prove that if a solution of an equation of KdV type is bounded above by a traveling wave with an amplitude that decays faster than a given linear exponential then it must be zero. We assume no restrictions neither on the size nor in the direction of the speed of the traveling wave. 
C. E. Kenig, G. Ponce, L. Vega
math.AP