Soliton solutions to the Sawada--Kotera equation
Exactly Solvable and Integrable Systems
2025-09-15 v2
Abstract
We consider the direct and inverse scattering problems for the third-order differential equation in the reflectionless case. We formulate a corresponding Riemann--Hilbert problem using input consisting of the bound-state poles of a transmission coefficient and the bound-state dependency constants. With the time-evolved dependency constants, using the solution to the Riemann--Hilbert problem, we construct soliton solutions to an integrable system of fifth-order nonlinear partial differential equations. By imposing some appropriate restrictions on the dependency constants, we show that those soliton solutions yield soliton solutions to the Sawada--Kotera equation.
Keywords
Cite
@article{arxiv.2509.01009,
title = {Soliton solutions to the Sawada--Kotera equation},
author = {Tuncay Aktosun and Abdon E. Choque-Rivero and Ivan Toledo and Mehmet Unlu},
journal= {arXiv preprint arXiv:2509.01009},
year = {2025}
}
Comments
28 pages, 5 figures