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Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations
Point classification the second order ODE's Ruslan Sharipov Painleve equations
2012/4/17
This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter...
On the classification of scalar evolutionary integrable equations in $2+1$ dimensions
On the classification scalar evolutionary integrable equations $2+1$ dimensions
2010/11/10
We consider evolutionary equations of the form $u_t=F(u, w)$ where $w=D_x^{-1}D_yu$ is the nonlocality, and the right hand side $F$ is polynomial in the derivatives of $u$ and $w$. The recent paper \c...
Preliminary group classification for generalized inviscid Burger's equation
Burgers’ equation Equivalence transformations Lie symmetries
2010/12/9
Preliminary group classification for a class of generalized inviscid Burger’s equa-tions in the general form ut+g(x, u)ux = f(x, u) is given and additional equivalence transformations are found. Adduc...