What question did this study set out to answer?

The aim is to study a new variable-coefficients integrable system derived from non-isospectral vector fields and to explore its properties.

May 10, 2026

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

Key Points

The aim is to study a new variable-coefficients integrable system derived from non-isospectral vector fields and to explore its properties.
Introduced a pair of two-dimensional non-isospectral vector fields.
Utilized the inverse scattering transform (IST) for the Cauchy problem analysis.
Employed the Riemann–Hilbert method to construct localized solutions.
Characterized a new (2 + 1)-dimensional generalized variable-coefficients Pavlov system.
Analyzed the large behavior of solutions, revealing significant properties.
Constructed implicit solutions, contributing to the understanding of the gVCP system.

Abstract

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.

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