Riemann–Hilbert Problem and Inverse Scattering Analysis for a New Generalized Variable‐Coefficients Pavlov System

ABSTRACT In this paper, we introduce a pair of two‐dimensional non‐isospectral vector fields whose commutation gives rise to a new variable‐coefficients integrable system which can reduce to the well‐known Pavlov equation. We refer to the new integrable system as the (2 + 1)‐dimensional generalized variable‐coefficients Pavlov (gVCP) system: (a) studying the inverse scattering and Cauchy problems via the inverse scattering transform (IST); (b) constructing the localized solutions of the gVCP via the Riemann–Hilbert (RH) method; (c) analyzing the large behavior of the solutions of the Cauchy problem for the gVCP system; (d) characterizing a class of implicit solutions of the gVCP system.