We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the Korteweg–de Vries equation, we show how the Gaussian decay emerges in the inverse scattering formalism.

• Received 18 March 1998

DOI:https://doi.org/10.1103/PhysRevE.58.7924