Radiative Decay of Weakly Nonlocal Solitary Waves

Abstract

A nanopteron is similar to a classical solitary wave except that it does not decay to zero as | x |→ 0, but to some form of radiation. It is a coherent structures which is independent of time except for a steady translation at a phase speed c. The amplitude of the wings is α, the “radiation coefficient”. For nanopterons, α is an exponential function of 1/∈ where ∈ is a small parameter that measures the amplitude and width of the core of the solitary wave.

“We have presented arguments that oceanic rings will generally lose energy, albeit slowly, by radiation of Rossby waves ⋯ The concept of the solitary eddy, then, has both virtues and flaws. Such models present clearly the fact that nonlinearity can be organizing, rather than causing decorrelation. But we need to recognize the simplifications which are made in arriving at an isolated solution and the fact that there will generally be leakage from the 'isolated' structure into an associated wave field.”

— Glenn R. Flierl (1994)