Abstract
In this work we study an eighth-order KdV-type equations in (1+1) and (2+1) dimensions. The new equations are derived from the KdV6 hierarchy. We show that these equations give multiple soliton solutions the same as the multiple soliton solutions of the KdV6 hierarchy except for the dispersion relations.
[1] W. Hereman, A. Nuseir, Math. Comput. Simulat. 43, 13 (1997) http://dx.doi.org/10.1016/S0378-4754(96)00053-510.1016/S0378-4754(96)00053-5Search in Google Scholar
[2] A.S. Fokas, Stud. Appl. Math. 77, 253 (1987) 10.1002/sapm1987773253Search in Google Scholar
[3] P.J. Olver, J. Math. Phys. 18, 1212 (1977) http://dx.doi.org/10.1063/1.52339310.1063/1.523393Search in Google Scholar
[4] B.A. Kupershmidt, Phys. Lett. A 372, 2634 (2008) http://dx.doi.org/10.1016/j.physleta.2007.12.01910.1016/j.physleta.2007.12.019Search in Google Scholar
[5] X. Geng, B. Xue, Appl. Math. Comput. (in press) Search in Google Scholar
[6] R. Hirota, The Direct Method in Soliton Theory, (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO978051154304310.1017/CBO9780511543043Search in Google Scholar
[7] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971) http://dx.doi.org/10.1103/PhysRevLett.27.119210.1103/PhysRevLett.27.1192Search in Google Scholar
[8] J. Hietarinta, J. Math. Phys. 28, 1732 (1987) http://dx.doi.org/10.1063/1.52781510.1063/1.527815Search in Google Scholar
[9] J. Hietarinta, J. Math. Phys. 28, 2094 (1987) http://dx.doi.org/10.1063/1.52742110.1063/1.527421Search in Google Scholar
[10] C.M. Khalique, A. Biswas, Phys. Lett. A 373, 2047 (2009) http://dx.doi.org/10.1016/j.physleta.2009.04.01110.1016/j.physleta.2009.04.011Search in Google Scholar
[11] K.R. Adem, C.M. Khalique, Nonlinear. Anal.-Real 13, 1692 (2012) http://dx.doi.org/10.1016/j.nonrwa.2011.12.00110.1016/j.nonrwa.2011.12.001Search in Google Scholar
[12] A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theorem, (Springer and HEP, Berlin, 2009) http://dx.doi.org/10.1007/978-3-642-00251-910.1007/978-3-642-00251-9Search in Google Scholar
[13] A.M. Wazwaz, Appl. Math. Comput. 204, 963 (2008) http://dx.doi.org/10.1016/j.amc.2008.08.00710.1016/j.amc.2008.08.007Search in Google Scholar
[14] A.M. Wazwaz, Commun. Nonlinear. Sci. 15, 1466 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.06.02410.1016/j.cnsns.2009.06.024Search in Google Scholar
[15] A.M. Wazwaz, Can. J. Phys. 87, 1227 (2010) http://dx.doi.org/10.1139/P09-10910.1139/P09-109Search in Google Scholar
[16] A.M. Wazwaz, Appl. Math. Comput. 199, 133 (2008) http://dx.doi.org/10.1016/j.amc.2007.09.03410.1016/j.amc.2007.09.034Search in Google Scholar
[17] A.M. Wazwaz, Appl. Math. Comput. 200, 437 (2008) http://dx.doi.org/10.1016/j.amc.2007.11.03210.1016/j.amc.2007.11.032Search in Google Scholar
[18] A.M. Wazwaz, Appl. Math. Comput. 201, 168 (2008) http://dx.doi.org/10.1016/j.amc.2007.12.00910.1016/j.amc.2007.12.009Search in Google Scholar
[19] A.M. Wazwaz, Appl. Math. Comput. 201, 489 (2008) http://dx.doi.org/10.1016/j.amc.2007.12.03710.1016/j.amc.2007.12.037Search in Google Scholar
[20] A.M. Wazwaz, Appl. Math. Comput. 201, 790 (2008) http://dx.doi.org/10.1016/j.amc.2008.01.01710.1016/j.amc.2008.01.017Search in Google Scholar
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