13 citations · 15 across the 3 of their papers we have counts for
5 papers
Relations for zeros of special polynomials associated to the Painleve equations
Nikolai A. Kudryashov, Maria V. Demina
A method for finding relations for the roots of polynomials is presented. Our approach allows us to get a number of relations for the zeros of the classical polynomials and for the…
Newton polygons for finding exact solutions
Nikolai A. Kudryashov, Maria V. Demina
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear diff…
Explicit form of the Yablonskii - Vorob'ev polynomials
Maria V. Demina, Nikolai A. Kudryashov
Special polynomials associated with rational solutions of the second Painlevé equation and other members of its hierarchy are discussed. New approach, which allows one to construct…
Polygons for finding exact solutions of nonlinear differential equations
Nikolai A. Kudryashov, Maria V. Demina
New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorith…
Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation
Maria V. Demina, Nikolai A. Kudryashov
Fourth - order analogue to the second Painlevé equation is studied. This equation has its origin in the modified Korteveg - de Vries equation of the fifth order when we look for it…