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In this paper, the Riemann–Hilbert approach is systematically established for the Newell-type long-wave–short-wave equation. Firstly, we start spectral analysis from the t-part of the Lax pair other than the x-part to obtain enough analytic spectral functions formulating the desired Riemann–Hilbert problems. The associated Riemann–Hilbert problems are determined by the t-part of the Lax pair with...
In this paper, a new coupled Gerdjikov–Ivanov derivative nonlinear Schrödinger equation is proposed and its integrability aspects are studied by utilizing the inverse scattering transform. Firstly, by performing spectral analysis of the Lax pair, Riemann–Hilbert problems are constructed and their zero structures are investigated. Secondly, by solving a particular Riemann–Hilbert problem corresponding...
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