On traveling solitary waves and absence of small data scattering for nonlinear half-wave equations

Bellazzini, Jacopo and Georgiev, Vladimir and Lenzmann, Enno and Visciglia, Nicola. (2019) On traveling solitary waves and absence of small data scattering for nonlinear half-wave equations. Communications in Mathematical Physics, 372 (2). pp. 713-732.

Full text not available from this repository.

Official URL: https://edoc.unibas.ch/75290/

Downloads: Statistics Overview


We consider nonlinear half-wave equations with focusing power-type nonlinearity
with exponents 1<p<∞ for d = 1 and 1<p<(d+1)/(d−1) for d ≥ 2. We study traveling solitary waves of the form
with frequency ω∈R, velocity v∈Rd, and some finite-energy profile Qv∈H1/2(Rd), Qv≢0. We prove that traveling solitary waves for speeds |v|≥1 do not exist. Furthermore, we generalize the non-existence result to the square root Klein–Gordon operator −Δ+m2−−−−−−−−√ and other nonlinearities. As a second main result, we show that small data scattering fails to hold for the focusing half-wave equation in any space dimension. The proof is based on the existence and properties of traveling solitary waves for speeds |v|<1. Finally, we discuss the energy-critical case when p=(d+1)/(d−1) in dimensions d ≥ 2.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Lenzmann)
UniBasel Contributors:Lenzmann, Enno
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer Nature
Note:Publication type according to Uni Basel Research Database: Journal article
Related URLs:
Identification Number:
Last Modified:30 Jun 2020 15:31
Deposited On:24 Jun 2020 13:19

Repository Staff Only: item control page