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Explicit integrable systems on two dimensional manifolds with a cubic first integral
Explicit integrable systems dimensional manifolds first integral
2010/4/2
A few years ago Selivanova gave an existence proof for some integrable models, in fact geodesic flows on two dimensional manifolds, with a cubic first integral. However the explicit form of these mod...
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system
arbitrary parameters integrable cases
2010/4/1
In this paper, we consider a second order nonlinear ordinary differential equation of the form
$\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$...
Comment on: "New exact solutions of the (3+1)-dimensional Burgers System" [Phys. Lett. A 373 (2009) 181]
(3+1)-dimensional Burgers System exact solutions
2010/4/6
We demonstrate that all exact solutions of the Riccati equation by Dai andWang [C.-Q. Dai, Y.-Y.Wang, Phys. Lett. A 373 (2009) 181-187] are not new and cannot be new because the general solution of th...