Abstract
In this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.
[1] X. Geng, C. Cao, H.H. Dai, J. Phys. A-Math. Gen. 34, 989 (2001) http://dx.doi.org/10.1088/0305-4470/34/5/30510.1088/0305-4470/34/5/305Search in Google Scholar
[2] X. Geng, J. Phys. A-Math. Gen. 36, 2289 (2003) http://dx.doi.org/10.1088/0305-4470/36/9/30710.1088/0305-4470/36/9/307Search in Google Scholar
[3] X. Geng, Y. Ma, Phys. Lett. A, 285 (2007) 10.1016/j.physleta.2007.04.099Search in Google Scholar
[4] J. Wu, Phys. Lett. A 373, 83 (2008) http://dx.doi.org/10.1016/j.physleta.2008.10.07110.1016/j.physleta.2008.10.071Search in Google Scholar
[5] B.B. Kadomtsev, V.I. Petviashvili, Soviet Physics - Doklady 15, 539 (1970) Search in Google Scholar
[6] M. Ito, J. Phys. Soc. Jpn. 49, 771 (1980) http://dx.doi.org/10.1143/JPSJ.49.77110.1143/JPSJ.49.771Search in Google Scholar
[7] R. Hirota, M. Ito, J. Phys. Soc. Jpn. 52, 744 (1983) http://dx.doi.org/10.1143/JPSJ.52.74410.1143/JPSJ.52.744Search in Google Scholar
[8] R. Hirota, J. Satsuma, J. Phys. Soc. Jpn. 40, 611 (1976) http://dx.doi.org/10.1143/JPSJ.40.61110.1143/JPSJ.40.611Search in Google Scholar
[9] R. Hirota, Prog. Theor. Phys. 52, 1498 (1974) http://dx.doi.org/10.1143/PTP.52.149810.1143/PTP.52.1498Search in Google Scholar
[10] 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
[11] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971) http://dx.doi.org/10.1103/PhysRevLett.27.119210.1103/PhysRevLett.27.1192Search in Google Scholar
[12] J. Hietarinta, J. Math. Phys. 28, 1732 (1987) http://dx.doi.org/10.1063/1.52781510.1063/1.527815Search in Google Scholar
[13] J. Hietarinta, J. Math. Phys. 28, 2094 (1987) http://dx.doi.org/10.1063/1.52742110.1063/1.527421Search in Google Scholar
[14] Y. Matsuno, Bilinear Transformation Method, (Academic Press, London, 1984) Search in Google Scholar
[15] Y. Matsuno, J. Phys. Soc. Jpn. 49, 787 (1980) http://dx.doi.org/10.1143/JPSJ.49.78710.1143/JPSJ.49.787Search in Google Scholar
[16] 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
[17] A. Scott, Encyclopedia of Nonlinear Sciences, (Routledge, New York, 2005) Search in Google Scholar
[18] A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, (Springer and HEP, Berlin and Peking, 2009) http://dx.doi.org/10.1007/978-3-642-00251-910.1007/978-3-642-00251-9Search in Google Scholar
[19] A.M. Wazwaz, Appl. Math. Comput. 190, 633 (2007) http://dx.doi.org/10.1016/j.amc.2007.01.05610.1016/j.amc.2007.01.056Search in Google Scholar
[20] 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
[21] 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
[22] 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
[23] 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
[24] 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
[25] A.M. Wazwaz, Appl. Math. Comput. 204, 20 (2008) http://dx.doi.org/10.1016/j.amc.2008.05.12610.1016/j.amc.2008.05.126Search in Google Scholar
[26] A.M. Wazwaz, Appl. Math. Comput. 204, 162 (2008) http://dx.doi.org/10.1016/j.amc.2008.06.01110.1016/j.amc.2008.06.011Search in Google Scholar
[27] A.M. Wazwaz, Appl. Math. Comput. 204, 817 (2008) http://dx.doi.org/10.1016/j.amc.2008.07.02510.1016/j.amc.2008.07.025Search in Google Scholar
[28] A.M. Wazwaz, Appl. Math. Comput. 204, 529 (2008) 10.1016/j.amc.2008.06.011Search in Google Scholar
[29] A.M. Wazwaz, Commun. Nonlinear Sci. 14, 2962 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.12.01810.1016/j.cnsns.2008.12.018Search in Google Scholar
[30] A.M. Wazwaz, Phys. Lett. A (in press) Search in Google Scholar
© 2010 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
