Nonexistence of subcritical solitary waves
We consider waves on the surface of an incompressible fluid, in particular localized solitary waves which travel at a constant speed. It is a long-standing conjecture that such waves must be "supercritical", traveling faster than infinitesimal periodic waves. While there are physical grounds for expecting subcritical solitary waves to be extremely rare, it seems impossible to turn these ideas into a rigorous proof. I will outline a surprisingly simple proof of this conjecture, which hinges instead on the properties of an auxiliary function related to momentum conservation. This is joint work with Vladimir Kozlov and Evgeniy Lokharu.
Password: “arizona” (all lower case)