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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...
On a Novel Class of Integrable ODEs Related to the Painlevé Equations
Painlev´ e equation conjugate Painlev´ e equation
2010/12/16
One of the authors has recently introduced the concept of conju-gate Hamiltonian systems: the solution of the equation h = H(p, q, t),where H is a given Hamiltonian containing t explicitly, yields the...
A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no...