Talk:Cnoidal wave

Tidbits
Both the non-linearity and dispersion must be small. Dispersion tries to separate different wavelengths, while non-linearity tries to bunch then up into a single crest. In simple terms, the small waves get picked up and carried by the longer waves, which are going only a bit faster. John Boyd (J. Phys. Oceanogr.) published a good summary of the m-factor in the KdV equation, when he showed the existence of the equatorial solotonic Rossby wave. m=0 is solotonic and m-=1 is cnoidal.

The pronunciation needs to be argued over. I've always called them "ca-noidal".220.244.89.140 (talk) 07:30, 16 October 2013 (UTC)


 * Indeed dispersion also has to be small: this is the reason why for the case of water waves only fairly long waves are covered (by the KdV and BBM equations). Regarding pronunciation: I do not know whether there is consensus. I have been taught: "kno-ee-dal". -- Crowsnest (talk) 16:57, 17 October 2013 (UTC)

Perturbation theory, Hamiltonain formalism
There do not seem to be any existing articles on deep water waves? (currently a red-link) and/or on the perturbation theory of KdV? Looking around, I see Airy wave theory which is about linearized deep-water waves (but in general KdV is non-linear). Stokes wave is about periodic waves (but in general, waves are not periodic). Waves and shallow water is a stub.

From what I can tell, the foundational paper that provides a Hamiltonian formalism for deep water waves is this: The perturbation theory for this is first worked out here: A nice review of the work is here: I'm trying to slap together Draft:Resonant interaction and am trying to figure out what WP articles already exist on these topics. Apparently, the primary wave in which waves interact in deep water is a four-wave resonant interaction. There is a wicked-cool experimental paper on this here: In general, there seem to be vast tracts of science literature on resonant interactions between solitons, cnoidal waves, wind, acoustic wave attentuation (e.g. submarine spy stuff) but not much in the way of foundational material on WP for any of this. Any help with Draft:Resonant interaction appreciated. 67.198.37.16 (talk) 19:38, 15 September 2020 (UTC)
 * Zakharov, V. 1968 Stability of periodic waves of finite amplitude on a surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–198.
 * Krasitskii, V. P. 1994 On reduced equations in the hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech. 272, 1 – 20.
 * Janssen, P. A. E. M. 2009 On some consequences of the canonical transformation in the hamiltonian theory of water waves. J. Fluid Mech. 637, 1–44.
 * F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaˆıtre, M. Berhanu, and E. Falcon, (2018) Observation of resonant interactions among surface gravity waves J. Fluid Mech.