Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908708597923840 |
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| author | Khare, Avinash Saxena, Avadh |
| author_facet | Khare, Avinash Saxena, Avadh |
| contents | We show that a fifth order KdV-type equation admits several real as well as complex parity-time reversal or PT-invariant solutions with linear superposition of quadratic functions involving Jacobi elliptic functions of the form ${\rm dn}^2(x,m)$, ${\rm cn}(x,m){\rm dn}(x,m)$, ${\rm sn}(x,m) {\rm cn}(x,m)$ and ${\rm sn}(x,m){\rm dn}(x,m)$. These results must be contrasted with only partial superposition of such functions in Korteweg-de Vries (KdV), $ϕ^3$ and a few other nonlinear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation Khare, Avinash Saxena, Avadh Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons We show that a fifth order KdV-type equation admits several real as well as complex parity-time reversal or PT-invariant solutions with linear superposition of quadratic functions involving Jacobi elliptic functions of the form ${\rm dn}^2(x,m)$, ${\rm cn}(x,m){\rm dn}(x,m)$, ${\rm sn}(x,m) {\rm cn}(x,m)$ and ${\rm sn}(x,m){\rm dn}(x,m)$. These results must be contrasted with only partial superposition of such functions in Korteweg-de Vries (KdV), $ϕ^3$ and a few other nonlinear equations. |
| title | Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2512.12173 |