This analysis observes energy decay patterns in large solutions of the dispersion generalized Benjamin-Ono equation, indicating key features of long-time behavior.
We study the long-time behavior of large solutions to the dispersion generalized Benjamin-Ono equation. By means of virial identities, we identify spatial regions around the origin, growing unbounded in time, not containing the soliton region in which every solution belonging in a suitable Sobolev space, necessarily decays to zero along some sequence of times. A similar result is also obtained for solutions of Benjamin equation, a model for gravity-capillary surface waves of the solitary type on deep water.
No takes yet. Share an insight, caveat, or question.
Ailton C. Nascimento (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: