Abstract
In this paper, the Riemann problem for the defocusing Hirota equation with weak dispersion is investigated with Whitham modulation theory. Hirota equation can effectively describe the realistic wave motion in dispersive medium. Via averaging Lagrangian method, the Whitham modulation equations in slow modulation form are obtained, which are characterized by wave parameters and reflects the dispersion relation in the original system. Besides, the modulation equations in Riemann invariant form are derived via finite-gap integration theory. Utilizing Whitham modulation equations parameterized by Riemann invariants, the basic structures of solutions for the Riemann problem for original system are acquired. According to the basic structure of the solutions, a complete solution classification corresponding to the initial data is given, including 121 categories. The results are verified by direct numerical simulation.
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