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 [9, 11] note. recent results on infinite soliton limit Korteweg–de Vries Kaup-Broer an appendix, classical 3D Laplace d’Alembert wave by Whittaker described. This appendix included elucidate analogy between method solutions.