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.

arXiv comment7 pages, accepted for publication in International Journal of Nonlinear Sciences and Numerical Simulation

References in corpus (2)

• Nonlinear Ordinary Differential Equations: A discussion on Symmetries and Singularities
• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector