An extended modified KdV equation and its Painlev, integrability

In this work we present an extended higher-order modified KdV equation. An analysis is carried out to show that this equation admits the Painlev, property. For this new integrable model, the one-soliton, two-soliton and three-soliton solutions are derived by using the simplified Hirota's direct method. We also demonstrate that one, two and three singular soliton solutions are possible for the defocusing form of this extended higher-order mKdV equation.