Singularity analysis and analytic solutions for the Benney-Gjevik equations

Abstract

We apply the Painlevé Test for the Benney and the Benney-Gjevik equations which describe waves in falling liquids. We prove that these two nonlinear 1+1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

7 pages, accepted for publication in International Journal of Nonlinear Sciences and Numerical Simulation

References in corpus (1)

• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector