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arXiv · 2509.01009

Soliton solutions to the Sawada--Kotera equation

Tuncay Aktosun·Abdon E. Choque-Rivero·Ivan Toledo·Mehmet Unlu
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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.

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Tuncay Aktosun, Abdon E. Choque-Rivero, Ivan Toledo, Mehmet Unlu. 2025-08-31. Soliton solutions to the Sawada--Kotera equation. https://arxiv.org/abs/2509.01009

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