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

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.