Self-similar Solutions Of Equations Research Articles

Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies

It is well known that the self-similar solutions of the Korteweg-de Vries equation and the modified Korteweg-de Vries equation are expressed via the solutions of the first and second Painleve equations. In this paper we solve this problem for all equations from the Korteveg-de Vries, modified Korteweg-de Vries, Kaup-Kupershmidt, Caudrey-Dodd-Gibbon and Fordy-Gibbons hierarchies. We show that the self-similar solutions of equations corresponding to hierarchies mentioned above can be found by means of the general solutions of higher-order Painleve hierarchies introduced more than ten years ago.

Turbulent free-convective jets: Numerical solution of model equations of transfer

Numerical solutions of self-similar equations for plane and axisymmetric free-convective jets are obtained using different semiempirical turbulence models. The results obtained are compared to the experimental data of other authors.

Self-similar solutions of equations of Korteweg -de Vries type

Self-similar solutions of equations of Korteweg -de Vries type