Blar i Bergen Open Research Archive på forfatter "Hussien Elkhorbatly, Bashar"
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The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech2 solutions
Hussien Elkhorbatly, Bashar (Journal article; Peer reviewed, 2024)In the context of the initial data and an amplitude parameter ε, we establish a local existence result for a highly nonlinear shallow water equation on the real line. This result holds in the space Hk as long as k > 5/2. ... -
Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations
Hussien Elkhorbatly, Bashar; Kalisch, Henrik (Journal article; Peer reviewed, 2024)It is shown that the Boussinesq–Peregrine system, which describes long waves of small amplitude at the surface of an inviscid fluid with variable depth, admits a number of approximate conservation equations. Notably, this ... -
Symmetric waves are traveling waves of some shallow water scalar equations
Hussien Elkhorbatly, Bashar (Journal article; Peer reviewed, 2023)Following a straightforward proof for symmetric solutions to be traveling waves by Pei (Exponential decay and symmetry of solitary waves to Degasperis-Procesi equation. Journal of Differential Equations. 2020;269(10):7730-7749), ...