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Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition
1.  Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 5202194 
2.  Graduate School of Science Department of Mathematical and Life Sciences, Hiroshima University, Kagamiyama, HigashiHiroshima, 7398526, Japan 
3.  Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, Shiga 5202194 
References:
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References:
[1] 
Meina Gao, Jianjun Liu. Quasiperiodic solutions for derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 21012123. doi: 10.3934/dcds.2012.32.2101 
[2] 
Kazumasa Fujiwara, Tohru Ozawa. On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation. Evolution Equations and Control Theory, 2018, 7 (2) : 275280. doi: 10.3934/eect.2018013 
[3] 
Phan Van Tin. On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions. Evolution Equations and Control Theory, 2022, 11 (3) : 837867. doi: 10.3934/eect.2021028 
[4] 
Michal Fečkan, Vassilis M. Rothos. Travelling waves of forced discrete nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems  S, 2011, 4 (5) : 11291145. doi: 10.3934/dcdss.2011.4.1129 
[5] 
Satoshi Kosugi, Yoshihisa Morita, Shoji Yotsutani. Stationary solutions to the onedimensional CahnHilliard equation: Proof by the complete elliptic integrals. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 609629. doi: 10.3934/dcds.2007.19.609 
[6] 
TsungFang Wu. Multiplicity of positive solutions for a semilinear elliptic equation in $R_+^N$ with nonlinear boundary condition. Communications on Pure and Applied Analysis, 2010, 9 (6) : 16751696. doi: 10.3934/cpaa.2010.9.1675 
[7] 
Razvan Mosincat, Haewon Yoon. Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 4780. doi: 10.3934/dcds.2020003 
[8] 
Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin. Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 93106. doi: 10.3934/dcds.1999.5.93 
[9] 
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 69436974. doi: 10.3934/dcds.2016102 
[10] 
Nakao Hayashi, Pavel I. Naumkin. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 383400. doi: 10.3934/dcds.1997.3.383 
[11] 
Pavel I. Naumkin, Isahi SánchezSuárez. Asymptotics for the higherorder derivative nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2021, 20 (4) : 14471478. doi: 10.3934/cpaa.2021028 
[12] 
Patrick Winkert. Multiplicity results for a class of elliptic problems with nonlinear boundary condition. Communications on Pure and Applied Analysis, 2013, 12 (2) : 785802. doi: 10.3934/cpaa.2013.12.785 
[13] 
Khadijah Sharaf. A perturbation result for a critical elliptic equation with zero Dirichlet boundary condition. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 16911706. doi: 10.3934/dcds.2017070 
[14] 
Vyacheslav A. Trofimov, Evgeny M. Trykin. A new way for decreasing of amplitude of wave reflected from artificial boundary condition for 1D nonlinear Schrödinger equation. Conference Publications, 2015, 2015 (special) : 10701078. doi: 10.3934/proc.2015.1070 
[15] 
Yue Liu. Existence of unstable standing waves for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2008, 7 (1) : 193209. doi: 10.3934/cpaa.2008.7.193 
[16] 
Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 525544. doi: 10.3934/dcds.2001.7.525 
[17] 
François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 12291247. doi: 10.3934/dcds.2009.25.1229 
[18] 
Zhaowei Lou, Jianguo Si, Shimin Wang. Invariant tori for the derivative nonlinear Schrödinger equation with nonlinear term depending on spatial variable. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022064 
[19] 
Nakao Hayashi, Pavel Naumkin. On the reduction of the modified BenjaminOno equation to the cubic derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 237255. doi: 10.3934/dcds.2002.8.237 
[20] 
Zihua Guo, Yifei Wu. Global wellposedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 257264. doi: 10.3934/dcds.2017010 
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