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 connect...

Abstract Despite outstanding accomplishments in catalyst discovery, finding new, more efficient, environmentally neutral, and noble metal-free catalysts remains challenging unsolved. Recently, complex solid solutions consisting of at least five different elements often named as high-entropy alloys have emerged a new class electrocatalysts for variety reactions. The multicomponent combinations f...