<p>All possible soliton solutions classification in the generalized KdV equation is given. It is proved that a solitonic solution can be one of four possible types: classical soliton (that is, sign-constant, with one extremum and two inflection points), pyramidal soliton (with a large number of inflection points), classical kink (a monotonic solution that goes to a constant other than zero at plus (minus) infinity with one inflection point) and pyramidal kink (like the classic one, but with a lot of inflection points). The conditions for the various types solitons appearance for certain equations classes with nonlinearity such as a generalized polynomial or the Tchebycheff system of smooth functions are clarified. Examples of equations with a nontrivial soliton form are given.</p>