Geodesic
About the modification of the Painlev\'e test for systems of nonlinear partial differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 367-376

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Following the formulation of [1] the Painlevé test is considered for the 2+1 dimensional model proposed in [2]. It is shown that for the model considered the standard ascending series procedure is correct only on the subset of solutions of the 1+1 dimensional reduction. The modified ascending series procedure is proposed giving a possibility to realize the procedure for a nonreduced case. Basing on this procedure, new representations of the Lax pair and the Backlund transformation are obtaioned. It is shown that the considered system is hamiltonian and some special (soliton's type) solutions are constructed. 
@article{TMF_1994_100_3_a4,
     author = {T. I. Garagash},
     title = {About the modification of the {Painlev\'e} test for systems of nonlinear partial differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {367--376},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a4/}
}
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T. I. Garagash. About the modification of the Painlev\'e test for systems of nonlinear partial differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 367-376. http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a4/