A Higher-Order Water-Wave Equation and the Method for Solving It

By a new technique, we have found another nonlinear evolution equation which can be solved exactly by inverse scattering techniques. This equation has a cubic :nonlinearity added to the Boussinesq equation and can .also be derived from the water-wave equations. This eigenvalue problem differs from any studied before, but in some aspects it is similar to, the sine-Gordon eigenvalue problem in laboratory coordinates. Also, the .solution to the inverse scattering problem is given.

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