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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.
Huang et al. (Tue,) studied this question.