Non-integrability of the Karabut system

In order to characterize the solitary wave in a fluid of finite depth, Witting introduced a specific power series (the Witting series). Karabut demonstrated that the problem of summation of the Witting series is brought to the integration of a particular system of ordinary differential equations and solved this system in the cases when the number of the equations is three or four. We give a simple proof that the Karabut system of five equations is already non-integrable in non-Hamiltonian sense using the Differential Galois approach.