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

2025/06/30 by Meulens, Rensley A. · 1 citation
#35A30 #35C08 #35Q35 #35Q40 #35Q51 #35Q53 #37K10 #37K25 #76D05 #Exactly Solvable and Integrable Systems (nlin.SI) #F.1.1 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #G.1.10 #G.1.7 #G.2.3 #I.6.5 #J.2 #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2506.23697

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.

Citations

• On the open Toda chain with external forcing
• Evolution by the vortex filament equation of curves with a corner
• Elliptic solutions of the Toda chain and a generalization of the Stieltjes-Carlitz polynomials
• The Discrete Nonlinear Schrödinger equation - 20 Years on

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• Exact Distributions for the Solutions of the Compressible Viscous Navier Stokes Differential Equations: An Application in the Aeronautical Industry

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