Painlevé analysis and pseudopotentials of the Schamel's equation (Q675724)

The authors carry out the Painlevé analysis for the Schamel equation \[ u_t+ u^{1/2} u_x+ u_{xxx} =0. \tag{1} \] The paper consists of three sections as follows: In the first section the authors show that (1) possesses the Painlevé property. In the second section they derive the Airy equation and the Harry-Dym equation by using the \(\varphi\)-equation. In the third section the authors use the method of \textit{M. C. Nucci} [J. Phys. A 21, 73-79 (1988; Zbl 0697.35134)] to derive the pseudopotentials for (1) by means of which they construct the Lax pair.