On the long-wave approximation of solitary waves in cylindrical coordinates

We address justification and solitary wave solutions of the cylindrical KdV equation which is formally derived as a long wave approximation of radially symmetric waves in a two-dimensional nonlinear dispersive system. For a regularized Boussinesq equation, we prove error estimates between true solutions of this equation and the associated cylindrical KdV approximation in the L2$$L^2$$-based spaces. The justification result holds in the spatial …