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Last week I went to the sea and observed some waves of the type pictured here

cross-swell
By Michel Griffon - Own work, CC BY 3.0, Link

And I wondered if they were solitons or not. I've seen more than once pictures of cross sea waves associated to solitons. However, I'm confused because cross sea waves look still periodic, even if they're quite spaced out between each other and the part of sea inside the squares seems almost perfectly flat. So are they solitons or not? Or something in between?

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There are multisoliton trains of waves. These look like KP solutions. Indeed this image is in the Wikipedia article on KP waves.

Here is another image of KP solitons on a beach

KP soliton

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Yes, they are solitons. Sometimes they called them line-soliton solutions or KP solitons. There is a book talking about the maths behind these types of solitons; see "KP Solitons and the Grassmannians."

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