Riemann–Hilbert approach of the coupled nonisospectral Gross–Pitaevskii system and its multi-component generalization

In this paper, we focus on the N-soliton solutions for the coupled nonisospectral Gross–Pitaevskii (GP) system. By using the Riemann–Hilbert approach, analyzing the spectral problem of the Lax pair, a kind of Riemann–Hilbert problem for a system of the coupled nonisospectral GP system is derived, and the N-soliton solutions for the equation under the conditions of irregularity and reflectionless cases also are presented. Moreover, the multi-component coupled nonisospectral GP system is generalized.