A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation

Abstract

Repetitive curling of the incompressible viscid Navier-Stokes differential equation leads to a higher-order diffusion equation. Substituting this equation into the Navier-Stokes differential equation transposes the latter into the Korteweg-de Vries-Burgers equation with the Weierstrass p-function as the soliton solution. However, a higher-order derivative of the studied variable produces the so-called N-soliton solution, which is comparable to the N-soliton solution of the Kadomtsev-Petviashvili equation.