5 research outputs found
On integrability of one third-order nonlinear evolution equation
We study one third-order nonlinear evolution equation, recently introduced by
Chou and Qu in a problem of plane curve motions, and find its transformation to
the modified Korteweg - de Vries equation, its zero-curvature representation
with an essential parameter, and its second-order recursion operator.Comment: 10 page
Coupled KdV equations of Hirota-Satsuma type
It is shown that the system of two coupled Korteweg-de Vries equations passes
the Painlev\'e test for integrability in nine distinct cases of its
coefficients. The integrability of eight cases is verified by direct
construction of Lax pairs, whereas for one case it remains unknown