Geodesic
On the connection of Kadomtaev--Petviashvili equation and Johnson equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 6, Tome 150 (1986), pp. 70-75

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The equivalence between the Kadomtaev–Petviashvili equation and Johnson equation for rapidly decreasing initial data is established. The Hamiltonian structure of Johnson–II equation as an example of above mentioned isomorphism is investigated. 
@article{ZNSL_1986_150_a7,
     author = {V. D. Lipovskii and V. B. Matveev and A. O. Smirnov},
     title = {On the connection of {Kadomtaev--Petviashvili} equation and {Johnson} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {70--75},
     publisher = {mathdoc},
     volume = {150},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_150_a7/}
}
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V. D. Lipovskii; V. B. Matveev; A. O. Smirnov. On the connection of Kadomtaev--Petviashvili equation and Johnson equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 6, Tome 150 (1986), pp. 70-75. http://geodesic.mathdoc.fr/item/ZNSL_1986_150_a7/