Abstract:
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.
Citation:
T. I. Garagash, “About the modification of the Painlevé test for systems of nonlinear partial differential equations”, TMF, 100:3 (1994), 367–376; Theoret. and Math. Phys., 100:3 (1994), 1075–1081
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\by T.~I.~Garagash
\paper About the modification of the Painlev\'e test for systems of nonlinear partial differential equations
\jour TMF
\yr 1994
\vol 100
\issue 3
\pages 367--376
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\jour Theoret. and Math. Phys.
\yr 1994
\vol 100
\issue 3
\pages 1075--1081
\crossref{https://doi.org/10.1007/BF01018572}
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Linking options:
https://www.mathnet.ru/eng/tmf1655
https://www.mathnet.ru/eng/tmf/v100/i3/p367
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