Soliton solutions associated with a class of third-order ordinary linear differential operators

2024/12/14 by Tuncay Aktosun, Aktosun, Tuncay, Abdon E. Choque‐Rivero +5 · 3 citations
Physics and Astronomy · #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2412.10971

Abstract

Explicit solutions to the related integrable nonlinear evolution equations are constructed by solving the inverse scattering problem in the reflectionless case for the third-order differential equation d³ψ/dx³+Q dψ/dx+Pψ=k³ψ, where Q and P are the potentials in the Schwartz class and k³ is the spectral parameter. The input data set used to solve the relevant inverse problem consists of the bound-state poles of a transmission coefficient and the corresponding bound-state dependency constants. Using the time-evolved dependency constants, explicit solutions to the related integrable evolution equations are obtained. In the special cases of the Sawada--Kotera equation and the modified bad Boussinesq equation, the method presented here explains the physical origin of the constants appearing in the relevant \mathbf N-soliton solutions algebraically constructed, but without any physical insight, by the bilinear method of Hirota.

Cited by

• Inverse scattering problem for the third-order equation on the line
• Inverse scattering problem for a third-order differential operator with double potential
• Soliton solutions to the Sawada--Kotera equation

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