The Whitham Modulation Solution of the Complex Modified KdV Equation

This paper primarily concerns the Whitham modulation equation of complex modified Korteweg–de Vries (cmKdV) with a step-like initial value. By utilizing Lax pair, we derive N-genus equations via averaging method. The can be integrated using hodograph transformation. We investigate Krichever’s algebro-geometric scheme to propose method for cmKdV integrable hierarchy and obtain velocities connection between Euler–Poisson–Darboux type linear overdetermined system, which determines solutions transformation, is constructed through Riemann integration, demonstrates that solved. Finally, value problem solved an exotic wave pattern discovered. results direct numerical simulation agree well theory solution, shows validity theory.