Journal of Nonlinear Mathematical Physics

Volume 1, Issue 1, February 1994

4. Antireduction and exact solutions of nonlinear heat equations

WILHELM FUSHCHYCH, RENAT ZHDANOV
Pages: 60 - 64
We construct a number of ansatzes that reduce one-dimensional nonlinear heat equations to systems of ordinary differential equations. Integrating these, we obtain new exact solution of nonlinear heat equations with various nonlinearities.

5. A completely integrable system associated with the Harry-Dym hierarchy

ZHIJUN QIAO
Pages: 65 - 74
By use of nonlinearization method about spectral problem, a classical completely integrable system associated with the Harry-Dym (HD) hierarchy is obtained. Furthermore, the involutive solution of each equation in the HD hierarchy is presented, in particular, the involutive solution of the well-known...

6. Symmetry reduction and exact solutions of the Navier-Stokes equations. I

WILHELM FUSHCHYCH, ROMAN POPOWYCH
Pages: 75 - 113
Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.