4 papers
Approximate Conservation Laws in the KdV Equation
Samer Israwi, Henrik Kalisch
The Korteweg-de Vries equation is known to yield a valid description of surface waves for waves of small amplitude and large wavelength. The equation features a number of conserved…
A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation
Samer Israwi, Henrik Kalisch
Consideration is given to the KdV equation as an approximate model for long waves of small amplitude at the free surface of an inviscid fluid. It is shown that there is an approxim…
Large Time existence For 1D Green-Naghdi equations
Samer Israwi
We consider here the Green-Naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves. We show that the solu…
Variable depth KDV equations and generalizations to more nonlinear regimes
Samer Israwi
We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It i…