In this paper, we establish local well-posedness for the Cauchy problem associated with the Korteweg–de Vries (KdV) equation on a general metric star graph. The graph comprises \(m+k\) semi-infinite edges: k negative half-lines and m positive half-lines, all joined at a common vertex. The choice of boundary conditions is compatible with the conditions determined by the semigroup theory considered by Mugonolo, Noja, and Seifert (APDE 2018). The crucial point in this work is to obtain the integral formula using the forcing operator method and the Fourier restriction method of Bourgain (GAFA 1993). This study extends the results obtained by Cavalcante (ZAMP 2018) for the specific case of the \({\mathcal {Y}}\) junction to a more general class of star graphs.
