Geodesic
Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 213-226 Cet article a éte moissonné depuis la source Math-Net.Ru

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A special solution of the Kadomtsev–Petviashvili equation $$u_{tx} + u_{xxxx} + 3u_{yy} + 3(u^2)_{xx} = 0,$$ that is a “nonlinear” analog of the special function of wave catastrophe corresponding to a singularity of swallowtail type is considered. On the basis of a symmetry analysis it is shown that the solution must simultaneously satisfy nonlinear ordinary differential equations with respect to all three independent variables. After “dressing” of the corresponding $\Psi$ function, equations with respect to a spectral parameter arise in a regular manner, and this indicates the possibility of applying the method of isomonodromic deformation. 
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     author = {B. I. Suleimanov and I. T. Habibullin},
     title = {Symmetries of {Kadomtsev{\textendash}Petviashvili} equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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B. I. Suleimanov; I. T. Habibullin. Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 213-226. http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a3/

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