Henrik Kalisch, University of Bergen
The KdV equation is the paradigm of an integrable partial differential equation and features various closed form solutions. One particularly useful solution is the so-called cnoidal wave, a steady periodic solution of the KdV given in terms of Jacobian elliptic functions.
The derivation of the KdV equation as a water-wave model can be used to obtain mathematical formulations for quantities such as mass transport, radiation stress and energy flux. The cnoidal wave can be specified in terms of measurable parameters such as waveheight, wave period and average fluid depth, and can be leveraged to analyze wave shoaling, wave breaking, infragravity-wave modulation, as well as stochastic properties of nearshore ocean waves.