The resulting
integro-differential equation can be reduced to the partial differential equation known as the Fornberg–Whitham equation:[6]
This equation is shown to allow for
peakon solutions – as a model for waves of limiting height – as well as the occurrence of wave breaking (
shock waves, absent in e.g. solutions of the Korteweg–de Vries equation).[6][3]
Debnath, L. (2005), Nonlinear Partial Differential Equations for Scientists and Engineers, Springer,
ISBN9780817643232
Fetecau, R.; Levy, Doron (2005), "Approximate Model Equations for Water Waves", Communications in Mathematical Sciences, 3 (2): 159–170,
doi:10.4310/CMS.2005.v3.n2.a4
The resulting
integro-differential equation can be reduced to the partial differential equation known as the Fornberg–Whitham equation:[6]
This equation is shown to allow for
peakon solutions – as a model for waves of limiting height – as well as the occurrence of wave breaking (
shock waves, absent in e.g. solutions of the Korteweg–de Vries equation).[6][3]
Debnath, L. (2005), Nonlinear Partial Differential Equations for Scientists and Engineers, Springer,
ISBN9780817643232
Fetecau, R.; Levy, Doron (2005), "Approximate Model Equations for Water Waves", Communications in Mathematical Sciences, 3 (2): 159–170,
doi:10.4310/CMS.2005.v3.n2.a4