Daniel Eriksson: Asymptotics of Boussinesq equation for long water waves

The Boussinesq equation is a nonlinear dispersive wave equation modelling water propagating in channels. Its rich mathematical properties being an integrable system enable us to derive approximative formulas for solutions valid for large times with decaying initial data defined on the real line. I will show simulations illustrating these results on the real line.

References:
Charlier, C., & Lenells, J. (2023). Direct and inverse scattering for the Boussinesq equation with solitons, arXiv:2302.14593 .
Charlier, C., & Lenells, J. (2023). The soliton resolution conjecture for the Boussinesq equation, arXiv:2303.10485 .
Charlier, C., & Lenells, J. (2022). On Boussinesq's equation for water waves, arXiv:2204.02365 .