Exact travelling nonlinear hydrodynamic waves

Exact travelling wave solutions for hydrodynamic waves in an incompressible medium are obtained when the wind is in asymmetry with the gravity. The governing system of equations are reduced to two ODEs with the help of an integral equation, obtained. These two equations are studied in the phase plane. We observe that the waves propagate in both directions when m -->-kG(2), where m and k are wavenumbers and G is the ratio of stratification parameters. The two ODEs obtained with the help of the integral equation, reduces to a nonlinear second order ODE which describes an one dimensional oscillator with nonlinear friction term.