Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Khare, Avinash, Saxena, Avadh
Formato: Preprint
Publicado: 2025
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866908708597923840
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