Solitary waves in a Whitham equation with small surface tension
Using a nonlocal version of the center-manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated solitary-wave solutions to the steady gravity-capillary Whitham equation with weak surface tension. Through the application of the center-manifold theorem, the nonlocal equation for the solitary wave profiles is reduced to
