Singularity analysis and analytic solutions for the Benney-Gjevik equations

We apply the Painleve 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.

Automated summary

This study applies the Painleve test to the Benney and Benney-Gjevik equations, which are used to describe waves in falling liquids. The research proves that these two nonlinear 1 + 1 evolution equations pass the singularity test for the traveling-wave solutions. Algebraic solutions based on Laurent expansions are presented.