The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles
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Shou-Fu Tian | Jin-Jie Yang | Xiao-Fan Zhang | Shou‐Fu Tian | Jin-Jie Yang | Xiao-Fan Zhang | Xiao-fan Zhang
[1] Wen-Xiu Ma,et al. Riemann–Hilbert problems andN-soliton solutions for a coupled mKdV system , 2018, Journal of Geometry and Physics.
[2] Zhenya Yan,et al. Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients , 2013, 1310.3544.
[3] Jingsong He,et al. The Darboux transformation of the derivative nonlinear Schrödinger equation , 2011, 1109.0674.
[4] B. Guo,et al. Long-time asymptotics for the Hirota equation on the half-line , 2018, Nonlinear Analysis.
[5] Zhenya Yan,et al. Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions , 2020, Commun. Nonlinear Sci. Numer. Simul..
[6] Jian Xu,et al. Long-time asymptotic for the Hirota equation via nonlinear steepest descent method , 2015 .
[7] Sahbi Keraani,et al. On the blow up phenomenon of the critical nonlinear Schrödinger equation , 2006 .
[8] B. Guo,et al. Solitons and rogue waves of the quartic nonlinear Schrödinger equation by Riemann–Hilbert approach , 2020 .
[9] Xianguo Geng,et al. Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation , 2017, Commun. Nonlinear Sci. Numer. Simul..
[10] Govind P. Agrawal,et al. Nonlinear Fiber Optics , 1989 .
[11] Xiao-Yong Wen,et al. Exotic Localized Vector Waves in a Two-Component Nonlinear Wave System , 2020, J. Nonlinear Sci..
[12] Jianke Yang,et al. Higher‐Order Solitons in the N‐Wave System , 2002, nlin/0204058.
[13] Gino Biondini,et al. Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions , 2014 .
[14] V. Zakharov,et al. Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media , 1970 .
[15] Valery S. Shchesnovich,et al. General soliton matrices in the Riemann–Hilbert problem for integrable nonlinear equations , 2003, nlin/0306027.
[16] Boling Guo,et al. Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation , 2012 .
[17] Xin Zhou,et al. Direct and inverse scattering transforms with arbitrary spectral singularities , 1989 .
[18] Zhenya Yan,et al. Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions , 2020 .
[19] E. Fan,et al. The unified transform method for the Sasa–Satsuma equation on the half-line , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[20] G. Biondini,et al. On the focusing non-linear Schrödinger equation with non-zero boundary conditions and double poles , 2017 .
[21] Deng-Shan Wang,et al. Integrable properties of the general coupled nonlinear Schrödinger equations , 2010 .
[22] Shou-Fu Tian,et al. Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method , 2017 .
[23] Shou‐Fu Tian,et al. Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition , 2017 .
[24] R. Hirota. Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .
[25] B. Guo,et al. Long-time asymptotics for the Kundu–Eckhaus equation on the half-line , 2017, Journal of Mathematical Physics.
[26] R. Hirota. Exact envelope‐soliton solutions of a nonlinear wave equation , 1973 .
[27] Shou-Fu Tian,et al. Initial–boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method☆ , 2017 .
[28] Adrian Ankiewicz,et al. Rogue waves and rational solutions of the Hirota equation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.
[29] C. Mee,et al. Exact solutions of the Hirota equation and vortex filaments motion , 2015 .
[30] X. Geng,et al. Riemann–Hilbert approach and N-soliton solutions for a generalized Sasa–Satsuma equation , 2016 .
[31] Jingsong He,et al. Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.
[32] A. Hasegawa,et al. Nonlinear pulse propagation in a monomode dielectric guide , 1987 .
[33] Q. P. Liu,et al. Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.
[34] Yuji Kodama,et al. Optical solitons in a monomode fiber , 1985 .
[35] D. Mihalache,et al. Painlevé analysis and bright solitary waves of the higher-order nonlinear Schrödinger equation containing third-order dispersion and self-steepening term , 1997 .
[36] Jianke Yang,et al. Nonlinear Waves in Integrable and Nonintegrable Systems , 2010, Mathematical modeling and computation.