Modeling, justification and mathematical analysis of models in oceanography are my research fields of interest. My research activity targets mainly the area of partial differential equations, my focus lies on studying dynamic properties of solutions to asymptotic nonlinear water waves models and nonlinear dispersive PDEs arising in fluid mechanics.

Keywords:   • Mathematical fluid dynamics
                  • Asymptotic nonlinear models for water-waves equations (mathematical modeling, well-posedness, solitary waves, conservation laws..)
                     • Behavior of solution of nonlinear dispersive PDEs (stability analysis of peakons, traveling waves, wave breaking, conservation laws..)

2024

• Hussien Elkhorbatly, Bashar; Kalisch, Henrik; Israwi, Samer (2024). Convergence of mechanical balance laws for water waves: from KdV to Euler. (external link)
• Hussien Elkhorbatly, Bashar (2024). Improved local existence result of the Green–Naghdi equations with the Coriolis effect. (external link)
• Hussien Elkhorbatly, Bashar (2024). The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech ² solutions. (external link)

2023

• Hussien Elkhorbatly, Bashar (2023). Exact traveling wave solutions of a geophysical Boussinesq system. (external link)
• Hussien Elkhorbatly, Bashar; Kalisch, Henrik (2023). Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations. (external link)

2022

• Hussien Elkhorbatly, Bashar (2022). Symmetric waves are traveling waves of some shallow water scalar equations. (external link)

See a complete overview of publications in Cristin.