Nonlinear Fourier Transforms for the Sawada–Kotera Equation on the Line

2025/07/01 by Lin Huang, Deng‐Shan Wang, Xiaodong Zhu · 1 citation
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems

paper · doi:10.1111/sapm.70075

Abstract

ABSTRACT This paper presents a Riemann–Hilbert (RH) problem formalism for the initial value problem of the Sawada–Kotera equation defined on the real line. Assuming the existence of a solution, we establish that this solution can be effectively represented by solving a matrix RH problem. Notably, the formulation of this RH problem involves four spectral functions: , , , and , which are obtained via a nonlinear Fourier transform applied to the initial data. Furthermore, this study conducts a detailed spectral analysis, providing a foundation for the application of the nonlinear steepest descent method to determine the long‐time asymptotic behavior of solutions to the Sawada–Kotera equation on the real line.

Citations

• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψxxx + 6Qψx + 6Rψ = λψ

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• Riemann-Hilbert construction of N-soliton solutions for the n-component reverse-space-time nonlocal generalized Sasa-Satsuma system

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