×

zbMATH — the first resource for mathematics

Bell-polynomial approach and soliton solutions for some higher-order Korteweg-de Vries equations in fluid mechanics, plasma physics and lattice dynamics. (English) Zbl 1330.35381
MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
Software:
PDEBellII
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Miao Q., Wang Y.H., Chen Y. and Yang Y.Q. 2014 Comput. Phys. Commun.185 357 · Zbl 1344.37003 · doi:10.1016/j.cpc.2013.09.005
[2] Lü X. and Lin F.H. 2016 Commun. Nonlinear Sci. Numer Simulat.32 241 · doi:10.1016/j.cnsns.2015.08.008
[3] Lü X. 2015 Nonlinear Dyn.81 239 · Zbl 1347.35211 · doi:10.1007/s11071-015-1985-5
[4] Ganji D.D. and Abdollahzadeh M. 2008 Appl. Math. Comput.206 438 · Zbl 1160.35516 · doi:10.1016/j.amc.2008.09.033
[5] Lü X. 2013 Chaos23 033137:1-8
[6] Lü X. and Li J. 2014 Nonlinear Dyn.77 135 · Zbl 1314.37049 · doi:10.1007/s11071-014-1279-3
[7] Lü X. and Peng M.S. 2013 Commun. Nonlinear Sci. Numer Simulat.18 2304 · Zbl 1304.35030 · doi:10.1016/j.cnsns.2012.11.006
[8] Whitham G. 1974 Linear and Nonlinear Waves (New York: Wiley)
[9] Hasegawa A. 1975 Plasma Instabilities and Nonlinear Effects (Berlin: Springer-Verlag) · doi:10.1007/978-3-642-65980-5
[10] Eilenberger G. 1983 Solitons (Berlin: Springer-Verlag) · Zbl 0455.35001
[11] Porsezian K. and Kuriakose V.C. 2003 Optical Solitons: Theoretical and Experimental Challenges (New York: Springer Press) · doi:10.1007/3-540-36141-3
[12] Kivshar Y.S. and Agrawal G.P. 2003 Optical Solitons from Fibers to Photonic Crystals (New York: Academic Press)
[13] Lü X. 2014 Commun. Nonlinear Sci. Numer Simulat.19 3969 · doi:10.1016/j.cnsns.2014.03.013
[14] Lü X., Ma W.X., Yu J., Liu F. and Khalique C.M. 2015 Nonlinear Dyn.82 1121
[15] Lü X., Ma W.X., Yu J. and Khalique C.M. 2016 Commun. Nonlinear Sci. Numer. Simulat.31 40 · doi:10.1016/j.cnsns.2015.07.007
[16] Korteweg D.J. and Vries G. de 1895 Phil. Mag.39 422 · doi:10.1080/14786449508620739
[17] Ablowitz M.J. and Clarkson P.A. 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press) · Zbl 0762.35001 · doi:10.1017/CBO9780511623998
[18] Ablowitz M.J. and Segur H. 1981 Solitons and the Inverse Scattering Transform (Philadelphia: Society for Industrial and Applied Mathematics) · Zbl 0472.35002 · doi:10.1137/1.9781611970883
[19] Lü X. and Peng M.S. 2013 Chaos23 013122:1-7
[20] Lü X. 2014 Nonlinear Dyn.76 161 · Zbl 1319.35222 · doi:10.1007/s11071-013-1118-y
[21] Lü X., Tian B., Sun K. and Wang P. 2010 J. Math. Phys.51 113506:1-8
[22] Lü X., Lin F.H. and Qi F.H. 2015 Appl. Math. Model.39 3221 · doi:10.1016/j.apm.2014.10.046
[23] Lü X., Ma W.X. and Khalique C.M. 2015 Appl. Math. Lett.50 37 · Zbl 1327.35341 · doi:10.1016/j.aml.2015.06.003
[24] Bell E.T. 1934 Ann. Math.35 258 · Zbl 0009.21202 · doi:10.2307/1968431
[25] Gilson C., Lambert F., Nimmo J. and Willox R. 1996 Proc. R. Soc. Lond. A 452 223 · Zbl 0868.35101 · doi:10.1098/rspa.1996.0013
[26] Lambert F. and Springael J. 1997 J. Phys. Soc. Jpn.66 2211 · Zbl 0947.37052 · doi:10.1143/JPSJ.66.2211
[27] Hu X.R. and Chen Y. 2011 Commun. Theor. Phys.56 218
[28] Wang Y.H. and Chen Y. 2013 Chin. Phys. B 22 050509
[29] Marchant T.R. 2002 Studies in Applied Mathematics109 1 · Zbl 1152.76343 · doi:10.1111/1467-9590.00001
[30] Korteweg D.J. and de Vries G. 1895 Philos. Mag.39 422 · doi:10.1080/14786449508620739
[31] Akylas T.R. 1984 J. Fluid Mech.141 455 · Zbl 0551.76018 · doi:10.1017/S0022112084000926
[32] Hai W. and Xiao Y. 1995 Phys. Lett. A 208 79 · Zbl 1020.35520 · doi:10.1016/0375-9601(95)00729-M
[33] Gotkas U. and Hereman W. 1997 J. Symbolic Computation24 591 · Zbl 0891.65129 · doi:10.1006/jsco.1997.0154
[34] Pomeau Y., Ramani A. and Grammaticos B. 1988 Phys. D 31 127 · Zbl 0695.35161 · doi:10.1016/0167-2789(88)90018-8
[35] Tamer A.A., Magdy A.E.T. and Zoheiry H.E. 2007 J. Comput. Appl. Math.207 73 · Zbl 1119.65095 · doi:10.1016/j.cam.2006.07.024
[36] Soliman A.A. 2006 Chaos, Solitons & Fractals29 294 · Zbl 1099.35521 · doi:10.1016/j.chaos.2005.08.054
[37] Darvishi M.T., Kheybari S. and Khani F. 2007 Int. J. Contemp. Math. Sciences2 1097
[38] Yao R.X., Xu G.Q. and Li Z.B. 2004 Commun. Theor. Phys.41 487
[39] Özer M.N., Tascan F. and Koparan M. 2010 Nonlinear. Anal.11 2619 · Zbl 1194.35422 · doi:10.1016/j.nonrwa.2009.09.009
[40] Aslan I. and Özis T. 2009 Appl. Math. Comput.211 531 · Zbl 1162.65391 · doi:10.1016/j.amc.2009.01.075
[41] Wazwaz A.M. 2008 Appl. Math. Comput.203 277 · Zbl 1157.65461 · doi:10.1016/j.amc.2008.04.040
[42] Wazwaz A.M. 2008 Appl. Math. Comput.206 1005 · Zbl 1188.65141 · doi:10.1016/j.amc.2008.09.011
[43] Hirota R. 1971 Phys. Rev. Lett.27 1192 · Zbl 1168.35423 · doi:10.1103/PhysRevLett.27.1192
[44] Liu L.C., Tian B., Qin B., Lü X., Lin Z.Q. and Liu W.J. 2012 Commun. Nonlinear Sci. Numer Simulat.17 2394 · Zbl 1252.35243 · doi:10.1016/j.cnsns.2011.10.026
[45] Hirota R. 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press) · doi:10.1017/CBO9780511543043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.