Correction to: On solutions to the nonlocal $${\overline{\partial }}$$-problem and (2+1) dimensional completely integrable systems

In this short note we discuss a new formula for solving the nonlocal $\overline{\partial}$-problem, and application to Manakov--Zakharov dressing method. We then explicitly apply complex (2+1)D Kadomtsev--Petviashvili equation completely integrable generalization of Kaup--Broer (or Kaup--Boussinesq) system. will also how real (1+1)D solutions are expressed using formalism. It is simple express formalism finite gap primitive from [10], [8] note. recent results on infinite soliton limit Korteweg--de Vries an appendix, classical 3D Laplace d'Alembert wave by Whittaker described. This appendix included elucidate analogy between method solutions.