  In this note, we discuss the existence of analytic solutions to the nonlinear
wave equations of the higher order than the ubiquitous Korteweg-de Vries (KdV)
equation. First, we recall our recent results which show that the extended KdV
equation (KdV2), that is, the equation obtained within second-order
perturbation approach possesses three kinds of analytic solutions. These
solutions have the same functional form as the corresponding KdV solutions. We
show, however, that the most intriguing multi-soliton solutions, known for the
KdV equation, do not exist for KdV2. Moreover, we show that for the equations
obtained in the third order perturbation approach (and then in any higher
order) analytic solutions in the forms known from KdV theory do not exist.
