Soliton, Positon and Negaton Solutions of Extended KdV Equation

Darboux transformation (DT) provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV (eKdV) equation, by which some new solutions such as singular soliton, negaton, and positon solutions arecomputed for the eKdV equation. We rediscover the soliton solutionwith finite-amplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys.89 (1999) 173] and discuss the difference betweenthis soliton and the singular soliton. We clarify the relationshipbetween the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail.