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In this work, the double and triple poles soliton solutions for theGerdjikov-Ivanov(GI) type of derivative nonlinear Schr\"{o}dinger equation withzero boundary conditions(ZBCs) and nonzero boundary conditions(NZBCs) arestudied via Riemann-Hilbert (RH) method. Though spectral problem analysis, wefirst give out the Jost function and scattering matrix under ZBCs and NZBCs.Then according to the analyticity, symmetry and asymptotic behavior of Jostfunction and scattering matrix, the Riemann-Hilbert problem(RHP) with ZBCs andNZBCs are constructed. Further, the obtained RHP with ZBCs and NZBCs can besolved in the case that reflection coefficients have double or triple poles.Finally, we derive the general precise formulae of N-double and N-triple polessolutions corresponding to ZBCs and NZBCs, respectively. The dynamicalbehaviors for these solutions are further discussed by image simulation.

journal of mathematical physics

Double and triple poles solutions for the Gerdjikov-Ivanov type of  derivative nonlinear Schr\"{o}dinger equation with zero/nonzero boundary  conditions