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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 
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J. V. Armitage and W. F. Eberlein, "Elliptic Functions ", Cambridge University Press, Cambridge, 2006. Google Scholar 
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S. Herr, On the Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition, Int. Math. Res. Not., (2006), article 96763. Google Scholar 
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H.Ikeda, K.Kondo, H.Okamoto and S.Yotsutani, On the global branches of the solutions to a nonlocal boundaryvalue problem arising in Oseen's spiral flows, Commun. Pure Appl. Anal., 2 (2003), no.3, 381390. Google Scholar 
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K. Imamura, Stability and bifurcation of periodic traveling waves in a derivative nonlinear Schrödingier equation, Hiroshima Math. J., 40 (2010), no. 2, 185  203. Google Scholar 
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S.Kosugi, Y.Morita and S.Yotsutani, A complete bifurcation diagram of the GinzburgLandau equation with periodic boundary conditions, Commun. Pure Appl. Anal., 4 (2005), no.3, 665682. Google Scholar 
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Y.Lou, WM.Ni and S.Yotsutani, On a limiting system in the LotkaVolterra competition with crossdiffusion. Partial differential equations and applications, Discrete Contin. Dyn. Syst., 10 (2004), no.12, 435458. Google Scholar 
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M.Murai, W. Matsumoto and S.Yotsutani, Representation formula for the plane closed elastic curves, Discrete Contin. Dyn. Syst. Supplement 2013, AIMS, (2013), 565585. Google Scholar 
show all references
References:
[1] 
J. V. Armitage and W. F. Eberlein, "Elliptic Functions ", Cambridge University Press, Cambridge, 2006. Google Scholar 
[2] 
S. Herr, On the Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition, Int. Math. Res. Not., (2006), article 96763. Google Scholar 
[3] 
H.Ikeda, K.Kondo, H.Okamoto and S.Yotsutani, On the global branches of the solutions to a nonlocal boundaryvalue problem arising in Oseen's spiral flows, Commun. Pure Appl. Anal., 2 (2003), no.3, 381390. Google Scholar 
[4] 
K. Imamura, Stability and bifurcation of periodic traveling waves in a derivative nonlinear Schrödingier equation, Hiroshima Math. J., 40 (2010), no. 2, 185  203. Google Scholar 
[5] 
S.Kosugi, Y.Morita and S.Yotsutani, A complete bifurcation diagram of the GinzburgLandau equation with periodic boundary conditions, Commun. Pure Appl. Anal., 4 (2005), no.3, 665682. Google Scholar 
[6] 
Y.Lou, WM.Ni and S.Yotsutani, On a limiting system in the LotkaVolterra competition with crossdiffusion. Partial differential equations and applications, Discrete Contin. Dyn. Syst., 10 (2004), no.12, 435458. Google Scholar 
[7] 
M.Murai, W. Matsumoto and S.Yotsutani, Representation formula for the plane closed elastic curves, Discrete Contin. Dyn. Syst. Supplement 2013, AIMS, (2013), 565585. Google Scholar 
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