An eighth-order KdV-type equation in (1+1) and (2+1) dimensions: multiple soliton solutions

• Authors: Abdul-Majid Wazwaz
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

KdV6 equation; simplified Hirota’s method; solitons; resonance

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 1
• Pages: 143-146

Dates

published

1 - 1 - 2013

online

15 - 1 - 2013

Contributors

author

Abdul-Majid Wazwaz

• Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

References

• [1] W. Hereman, A. Nuseir, Math. Comput. Simulat. 43, 13 (1997) http://dx.doi.org/10.1016/S0378-4754(96)00053-5[Crossref]
• [2] A.S. Fokas, Stud. Appl. Math. 77, 253 (1987)
• [3] P.J. Olver, J. Math. Phys. 18, 1212 (1977) http://dx.doi.org/10.1063/1.523393[Crossref]
• [4] B.A. Kupershmidt, Phys. Lett. A 372, 2634 (2008) http://dx.doi.org/10.1016/j.physleta.2007.12.019[Crossref]
• [5] X. Geng, B. Xue, Appl. Math. Comput. (in press)
• [6] R. Hirota, The Direct Method in Soliton Theory, (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511543043[Crossref]
• [7] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971) http://dx.doi.org/10.1103/PhysRevLett.27.1192[Crossref]
• [8] J. Hietarinta, J. Math. Phys. 28, 1732 (1987) http://dx.doi.org/10.1063/1.527815[Crossref]
• [9] J. Hietarinta, J. Math. Phys. 28, 2094 (1987) http://dx.doi.org/10.1063/1.527421[Crossref]
• [10] C.M. Khalique, A. Biswas, Phys. Lett. A 373, 2047 (2009) http://dx.doi.org/10.1016/j.physleta.2009.04.011[Crossref]
• [11] K.R. Adem, C.M. Khalique, Nonlinear. Anal.-Real 13, 1692 (2012) http://dx.doi.org/10.1016/j.nonrwa.2011.12.001[Crossref]
• [12] A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theorem, (Springer and HEP, Berlin, 2009) http://dx.doi.org/10.1007/978-3-642-00251-9[Crossref]
• [13] A.M. Wazwaz, Appl. Math. Comput. 204, 963 (2008) http://dx.doi.org/10.1016/j.amc.2008.08.007[Crossref]
• [14] A.M. Wazwaz, Commun. Nonlinear. Sci. 15, 1466 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.06.024[Crossref]
• [15] A.M. Wazwaz, Can. J. Phys. 87, 1227 (2010) http://dx.doi.org/10.1139/P09-109[Crossref]
• [16] A.M. Wazwaz, Appl. Math. Comput. 199, 133 (2008) http://dx.doi.org/10.1016/j.amc.2007.09.034[Crossref]
• [17] A.M. Wazwaz, Appl. Math. Comput. 200, 437 (2008) http://dx.doi.org/10.1016/j.amc.2007.11.032[Crossref]
• [18] A.M. Wazwaz, Appl. Math. Comput. 201, 168 (2008) http://dx.doi.org/10.1016/j.amc.2007.12.009[Crossref]
• [19] A.M. Wazwaz, Appl. Math. Comput. 201, 489 (2008) http://dx.doi.org/10.1016/j.amc.2007.12.037[Crossref]
• [20] A.M. Wazwaz, Appl. Math. Comput. 201, 790 (2008) http://dx.doi.org/10.1016/j.amc.2008.01.017[Crossref]

Identifiers

DOI

10.2478/s11534-012-0156-2