112 citations · 484 across the 23 of their papers we have counts for
24 papers
Superposition solutions to the extended KdV equation for water surface waves
Piotr Rozmej, Anna Karczewska, Eryk Infeld
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Altho…
Single soliton solution to the extended KdV equation over uneven depth
George Rowlands, Piotr Rozmej, Eryk Infeld +1
In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in approximate transformation of the equation governing wave motion over uneven…
Exact solitonic and periodic solutions of the extended KdV equation
Eryk Infeld, Anna Karczewska, George Rowlands +1
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include both higher order effects (…
Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas
Piotr Goldstein, Eryk Infeld
Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for st…
Adiabatic invariants of the extended KdV equation
Anna Karczewska, Piotr Rozmej, Eryk Infeld +1
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic i…
Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Is energy always an invariant?
Anna Karczewska, Piotr Rozmej, Eryk Infeld
It is well known that the KdV equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum and energy. Here we try to answ…