Dynamics of the Gross-Pitaevskii equation and related dispersive equations (A12#)

• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

The one-dimensional Gross-Pitaevskii equation models effectively the propagation of waves through a condensate of constant density. The nonzero boundary condition of finite density type at infinity causes mathematical challenges. The aim of this project is to study its dynamics in a well-established analytical framework and to extend the analytical tools and results to other related dispersive equations. In the last funding period, we obtained global wellposedness results for GP-equation, as well as Whitham approximation results for various dispersive equations. In the next funding period, we plan to establish the stability of soliton solutions and to improve the length of approximation times.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1173: Wave phenomena: analysis and numerics
• Applicant Institution: Karlsruher Institut für Technologie
• Project Heads: Dr. Xian Liao; Professor Dr. Guido Schneider