On global solutions of defocusing mKdV equation with specific initial data of critical regularity

Abstract We are concerned with the defocusing modified Korteweg–de Vries equation equipped particular type of irregular initial conditions that given as linear combination Dirac delta function and Cauchy principal value. For value problem we prove existence smooth self-similar solution, whose profile is Ablowitz–Segur solution second Painleve equation. Our method to use approach based on Riemann–Hilbert improve asymptotics these transcendents find desired by constructing its Stokes multipliers.