A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908428175147008 |
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| author | Meulens, Rensley A. |
| author_facet | Meulens, Rensley A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation Meulens, Rensley A. Exactly Solvable and Integrable Systems Mathematical Physics Fluid Dynamics 76D05, 35Q35, 35C08, 35Q53, 37K10, 35Q51, 35Q40, 37K25, 35A30 G.1.7; G.1.10; G.2.3; F.1.1; I.6.5; J.2 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. |
| title | A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Fluid Dynamics 76D05, 35Q35, 35C08, 35Q53, 37K10, 35Q51, 35Q40, 37K25, 35A30 G.1.7; G.1.10; G.2.3; F.1.1; I.6.5; J.2 |
| url | https://arxiv.org/abs/2506.23697 |