A Theorem on Boussinesq Solitons or Why Soliton Formation Sharpens Resonant Absorption and Why This Has Nothing to Do With Real Polymers

Abstract

Soliton formation has been proposed as an explanation for anomalously sharp resonances observed in DNA microwave absorption. We give an elementary, physical explanation of why line narrowing occurs for Boussinesq solitons. We consider real atoms bound by realistic chemical bonds and show that even under the assumption of the most favorable possible conditions, the soliton narrowing mechanism is a maximum correction of only a few percent. At each step of the argument, the simple calculations we show are either exact-in the sense of following the Boussinesq equation-or err on the side of emphasizing the soliton lifetime enhancement. Thus our results serve as an upper bound to any enhancement effects.