Integrating the loaded Hirota equation via the inverse scattering method

This study demonstrates that the inverse scattering transform method within the class of rapidly decreasing functions proves highly effective for solving the Cauchy problem for the loaded Hirota equation. The primary focus is on determining the time evolution of scattering data for the Dirac operator, which serves as the solution to the Cauchy problem for the loaded Hirota equation with potentials from the class of rapidly decaying functions.

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