On the Benjamin and Related Equations
Copyright policy )On the Benjamin and Related Equations
We consider in this paper various theoretical and numerical issues on classical one dimensional models of internal waves with surface tension.They concern the Cauchy problem, including the long time dynamic, localized solitons or multisolitons, the soliton resolution property. We survey known results, present a few new ones together with open questions and conjectures motivated by numerical simulations. A major issue is to emphasize the differences of the qualitative behavior of solutions with those of the same equations without the capillary term.
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Internal waves for incompressible inviscid fluids, Surface tension, Asymptotic behavior of solutions to PDEs, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, [MATH] Mathematics [math], PDEs in connection with fluid mechanics, Capillarity (surface tension) for incompressible inviscid fluids, Solitary waves for incompressible inviscid fluids, Benjamin equation, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), Soliton solutions, internal waves, surface tension, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, Internal waves, Analysis of PDEs (math.AP)
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Internal waves for incompressible inviscid fluids, Surface tension, Asymptotic behavior of solutions to PDEs, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, [MATH] Mathematics [math], PDEs in connection with fluid mechanics, Capillarity (surface tension) for incompressible inviscid fluids, Solitary waves for incompressible inviscid fluids, Benjamin equation, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), Soliton solutions, internal waves, surface tension, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, Internal waves, Analysis of PDEs (math.AP)
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!