arXiv subjects

Sergei Yu. Sakovich

Publications and source records attributed to Sergei Yu. Sakovich.

5 recordsLinked to original sources

arXiv2004

Singularity analysis of a spherical Kadomtsev-Petviashvili equation

The (2+1)-dimensional spherical Kadomtsev-Petviashvili (SKP) equation of J.-K. Xue [Phys. Lett. A 314:479-483 (2003)] fails the Painleve test for integrability at the highest resonance, where a nontrivial compatibility condition for recursion relations appears. This compatibility condition, however, is sufficiently weak and thus allows the SKP equation to possess an integrable (1+1)-dimensional reduction, which is detected by the Weiss method of truncated singular expansions.

nlin.SI↗

arXiv2001

Addendum to ``Coupled KdV Equations of Hirota-Satsuma Type'' (J. Nonlin. Math. Phys. Vol. 6, No.3 (1999), 255--262)

It is shown that one system of coupled KdV equations, found in J. Nonlin. Math. Phys., 1999, Vol.6, Nr.3, 255--262 [arXiv:solv-int/9901005] to possess the Painlevé property, is integrable but not new.

nlin.SI↗

arXiv2001

A system of four ODEs: the singularity analysis

The singularity analysis is carried out for a system of four first-order quadratic ODEs with a parameter, which was proposed recently by Golubchik and Sokolov. A transformation of dependent variables is revealed by the analysis, after which the transformed system possesses the Painlevé property and does not contain the parameter.

nlin.SI↗

arXiv1999

Coupled KdV equations of Hirota-Satsuma type

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlevé test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown.

solv-int↗

arXiv1998

On integrability of a (2+1)-dimensional perturbed Kdv equation

A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlevé test for integrability well, and its 4$\times $4 Lax pair with two spectral parameters is found. The results show that the Painlevé classification of coupled KdV equations by A. Karasu should be revised.

solv-int↗