Scattering theory for the Schrödinger–improved Boussinesq system in two space dimensions

Article type: Research Article

Authors: Shimomura, Akihiro

Affiliations: Department of Mathematics, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan E-mail: [email protected]

Abstract: In this paper, the scattering theory for the Schrödinger–improved Boussinesq system in two space dimensions is studied. The local Cauchy problem at infinite initial time of this system for given final data is considered, and the existence of a unique asymptotically free solution to this system is proved when the Schrödinger data is suitably small.

Keywords: Schrödinger–improved Boussinesq system, asymptotic behavior of solutions, scattering theory, asymptotically free solution

Journal: Asymptotic Analysis, vol. 51, no. 2, pp. 167-187, 2007