[1] Ablowitz, M.J., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering. In: London Mathematical Society Lecture Note Series, vol. 149. Cambridge University Press, Cambridge (1991)
[2] Ablowitz, M.J., Fokas, A.S.: Complex variables: introduction and applications. In: Cambridge Texts in Applied Mathematics, 2nd edn. Cambridge University Press, Cambridge (2003)
[3] Ablowitz, M.J., Segur, H.: Solitons and the inverse scattering transform. In: SIAM Studies in Applied Mathematics, vol. 4. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1981)
[4] Aktosun, T., Demontis, F., van der Mee, C.: Exact solutions to the focusing nonlinear Schrödinger equation. Inverse Prob. 23, 2171-2195 (2007)
[5] Beals, R., Coifman, R.R.: Scattering and inverse scattering for first order systems. Commun. Pure Appl. Math. 37, 39-90 (1984)
[6] Beals, R., Deift, P., Tomei, C.: Direct and inverse scattering on the line. In: Mathematical Surveys and Monographs, vol. 28. American Mathematical Society, Providence (1988)
[7] Bilman, D., Miller, P.D.: A robust inverse scattering transform for the focusing nonlinear Schrödinger equation. Commun. Pure Appl. Math. 72, 1722-1805 (2019)
[8] Biondini, G., Fagerstrom, E.: The integrable nature of modulational instability. SIAM J. Appl. Math. 75, 136-163 (2015)
[9] Biondini, G., Kovačič, G.: Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions. J. Math. Phys. 55, 031506 (2014)
[10] Biondini, G., Li, S., Mantzavinos, D.: Soliton trapping, transmission and wake in modulationally unstable media. Phys. Rev. E 98, 042211 (2018)
[11] Biondini, G., Li, S., Mantzavinos, D.: Long-time asymptotics for the focusing nonlinear Schrödinger equation with nonzero boundary conditions in the presence of a discrete spectrum. Commun. Math. Phys. 382, 1495-1577 (2021)
[12] Biondini, G., Li, S., Mantzavinos, D., Trillo, S.: Universal behavior of modulationally unstable media. SIAM Rev. 60, 888-908 (2018)
[13] Biondini, G., Lottes, J., Mantzavinos, D.: Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows. Stud. Appl. Math. 146, 371-439 (2021)
[14] Chen, M.S., Fan, E.G.: Riemann-Hilbert approach for discrete sine-Gordon equation with simple and double poles. Stud. Appl. Math. 148, 1180-1207 (2022)
[15] Chen, M.S., Fan, E.G., He, J.S.: Riemann-Hilbert approach and the soliton solutions of the discrete mKdV equations. Chaos Solitons Fractals 168, 113209 (2023)
[16] Demontis, F., Prinari, B., van der Mee, C., Vitale, F.: The inverse scattering transform for the defocusing nonlinear Schrödinger equations with nonzero boundary conditions. Stud. Appl. Math. 131, 1-40 (2013)
[17] Fokas, A.S.: A unified approach to boundary value problems. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 78. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2008)
[18] Fokas, A.S., Its, A.R.: The linearization of the initial-boundary value problem of the nonlinear Schröinger equation. SIAM J. Math. Anal. 27, 738-764 (1996)
[19] Kawata, T., Inoue, H.: Inverse scattering method for the nonlinear evolution equations under nonvanishing conditions. J. Phys. Soc. Jpn. 44, 1722-1729 (1978)
[20] Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N., Dudley, J.M.: The Peregrine soliton in nonlinear fibre optics. Nat. Phys. 6, 790-795 (2010)
[21] Liu, H., Shen, J., Geng, X.G.: Inverse scattering transformation for the \begin{document}$ N $\end{document}-component focusing nonlinear Schrödinger equation with nonzero boundary conditions. Lett. Math. Phys. 113, 23 (2023)
[22] Lyu, C., Liu, Q.P.: Multiple higher-order pole solutions of modified complex short pulse equation. Appl. Math. Lett. 141, 108518 (2023)
[23] Lyu, C., Qiu, D.Q., Liu, Q.P.: Riemann-Hilbert approach to two-component modified short-pulse system and its nonlocal reductions. Chaos 32, 093120 (2022)
[24] Ma, Y.C.: The perturbed plane-wave solutions of the cubic Schrödinger equation. Stud. Appl. Math. 60, 43-58 (1979)
[25] Olmedilla, E.: Multiple pole solutions of the nonlinear Schrödinger equation. Physica D 25, 330-346 (1987)
[26] Pichler, M., Biondini, G.: On the focusing non-linear Schrödinger equation with non-zero boundary conditions and double poles. IMA J. Appl. Math. 82, 131-151 (2017)
[27] Prinari, B., Ablowitz, M.J., Biondini, G.: Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions. J. Math. Phys. 47, 063508 (2006)
[28] Schiebold, C.: Asymptotics for the multiple pole solutions of the nonlinear Schrödinger equation. Nonlinearity 30, 2930-2981 (2017)
[29] Shchesnovich, V.S., Yang, J.K.: General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations. J. Math. Phys. 44, 4604-4639 (2003)
[30] Shchesnovich, V.S., Yang, J.K.: Higher-order solitons in the \begin{document}$ N $\end{document}-wave system. Stud. Appl. Math. 110, 297-332 (2003)
[31] Tsuru, H., Wadati, M.: The multiple pole solutions of the sine-Gordon equation. J. Phys. Soc. Jpn. 53, 2908-2921 (1984)
[32] Wadati, M., Ohkuma, K.: Multiple-pole solutions of the modified Korteweg-de Vries equation. J. Phys. Soc. Jpn. 51, 2029-2035 (1982)
[33] Zakharov, V.E., Ostrovsky, L.A.: Modulation instability: the beginning. Physica D 238, 540-548 (2009)
[34] Zakharov, V.E., Shabat, A.B.: Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62-69 (1972)
[35] Zhang, G.Q., Yan, Z.Y.: The derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions: inverse scattering transforms and \begin{document}$ n $\end{document}-double-pole solutions. J. Nonlinear Sci. 30, 3089-3127 (2020)
[36] Zhang, Y.S., Tao, X.X., Xu, S.W.: The bound-state soliton solutions of the complex modified KdV equation. Inverse Prob. 36, 065003 (2020)
[37] Zhang, Y.S., Tao, X.X., Yao, T.T., He, J.S.: The regularity of the multiple higher-order poles solitons of the NLS equation. Stud. Appl. Math. 145, 812-827 (2020)
[38] Zhou, X.: The Riemann-Hilbert problem and inverse scattering. SIAM J. Math. Anal. 20, 966-986 (1989)