Quasi-periodic solution of a new \((2+1)\)-dimensional coupled soliton equation (Q2716824)

This paper deals with a new \((2+1)\)-dimensional coupled mKdV equation that is important in physics and soliton theory. Through the nonlinearization of the Levi eigenvalue problems, the authors obtain a finite-dimensional integrable system. Here the generating function \({\mathcal F} (\lambda)\) approach plays a central role in the straightening of the flows, where the evolution of all \(F_m\)-flows is obtained simultaneously through the calculation of the evolution of the \({\mathcal F}(\lambda)\)-flow on Abelian varieties. Moreover, the authors obtain quasi-periodic solutions of the \((2+1)\)-coupled soliton equations by means of Riemann theta functions.