On a class of compact perturbations of the special pole-free joint solution of KdV and $P_I^2.$

B. Dubrovin, A. Minakov

We consider perturbations of the special pole-free joint solution $U(x,t)$ of the Korteweg--de Vries equation $u_t+u{u}_x+\frac{1}{12}{u}_{xxx}=0$ and $P_I^2$ equation $u_{xxxx}+10u_x^…