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

ABSTRACT

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.

COMMUNICATED BY:

• Der-Chen Edward Chang

Keywords:

• Coupled nonisospectral Gross–Pitaevskii system
• Riemann–Hilbert approach
• N-soliton solutions

AMS SUBJECT CLASSIFICATIONS:

• 35Q15
• 35G25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11371326 and No. 11975145).