×

The travelling wave solutions for non-linear initial-value problems using the homotopy perturbation method. (English) Zbl 1167.35493

Summary: We have used the homotopy perturbation method (HPM) to find the travelling wave solutions for some non-linear initial-value problems in the mathematical physics. These problems consist of the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrödinger KdV equations and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the HPM is very powerful, effective, convenient and quite accurate to the systems of non-linear equations. It is predicted that this method can be found widely applicable in engineering and physics.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
35B20 Perturbations in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Zayed EME, Int. J. Non-linear Sci. Numer. Simul. 5 pp 221– (2004) · Zbl 1401.35014 · doi:10.1515/IJNSNS.2004.5.3.221
[2] Abdusalam HA, Int. J. Non-linear Sci. Numer. Simul. 6 pp 99– (2005) · Zbl 1401.35012 · doi:10.1515/IJNSNS.2005.6.2.99
[3] Abassy TA, Int. J. Non-linear Sci. Numer. Simul. 5 pp 327– (2004) · Zbl 1401.65122 · doi:10.1515/IJNSNS.2004.5.4.327
[4] Liu HM, Int. J. Nonlinear Sci. Numer. Simul. 5 pp 95– (2004) · Zbl 06942051 · doi:10.1515/IJNSNS.2004.5.1.95
[5] DOI: 10.1016/S0020-7462(98)00048-1 · Zbl 1342.34005 · doi:10.1016/S0020-7462(98)00048-1
[6] Draganescu GE, Int. J. Non-linear Sci. Numer. Simul. 4 pp 219– (2004) · Zbl 06942016 · doi:10.1515/IJNSNS.2003.4.3.219
[7] DOI: 10.1016/S0020-7462(00)00116-5 · Zbl 1116.34320 · doi:10.1016/S0020-7462(00)00116-5
[8] DOI: 10.1016/S0020-7462(00)00117-7 · Zbl 1116.34321 · doi:10.1016/S0020-7462(00)00117-7
[9] He JH, Int. J. Nonlinear Sci. Numer. Simul. 2 pp 317– (2001) · Zbl 1072.34507 · doi:10.1515/IJNSNS.2001.2.4.317
[10] DOI: 10.1016/0022-247X(88)90170-9 · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[11] DOI: 10.1016/S0096-3003(97)10037-6 · Zbl 0942.65107 · doi:10.1016/S0096-3003(97)10037-6
[12] DOI: 10.1016/j.camwa.2006.12.041 · Zbl 1143.35360 · doi:10.1016/j.camwa.2006.12.041
[13] He JH, Gongcheng Yu Kexue Zhong de jinshi feixianxing feixi fangfa (in Chinese) (2002)
[14] DOI: 10.1103/PhysRevLett.90.174301 · doi:10.1103/PhysRevLett.90.174301
[15] Shen J, Int. J. Nonlinear Sci. Numer. Simul. 5 pp 397– (2004) · Zbl 1401.35276 · doi:10.1515/IJNSNS.2004.5.4.397
[16] Ma S, Int. J. Nonlinear Sci. Numer. Simul. 6 pp 13– (2005) · Zbl 1401.92032 · doi:10.1515/IJNSNS.2005.6.1.13
[17] Zhang Y, Int. J. Nonlinear Sci. Numer. Simul. 6 pp 63– (2005) · Zbl 1401.37058 · doi:10.1515/IJNSNS.2005.6.1.63
[18] Zhang Z, Int. J. Nonlinear Sci. Numer. Simul. 6 pp 81– (2005) · Zbl 1401.37057 · doi:10.1515/IJNSNS.2005.6.1.81
[19] Zheng Y, Int. J. Nonlinear Sci. Numer. Simul. 6 pp 87– (2005) · Zbl 1401.74196 · doi:10.1515/IJNSNS.2005.6.1.87
[20] DOI: 10.1016/S0375-9601(01)00161-X · Zbl 0984.37092 · doi:10.1016/S0375-9601(01)00161-X
[21] DOI: 10.1016/j.amc.2007.05.020 · Zbl 1132.65098 · doi:10.1016/j.amc.2007.05.020
[22] DOI: 10.1016/j.amc.2006.06.002 · Zbl 1107.65094 · doi:10.1016/j.amc.2006.06.002
[23] DOI: 10.1016/S0096-3003(03)00341-2 · Zbl 1039.65052 · doi:10.1016/S0096-3003(03)00341-2
[24] DOI: 10.1016/j.amc.2003.08.008 · Zbl 1062.65074 · doi:10.1016/j.amc.2003.08.008
[25] DOI: 10.1016/j.amc.2003.08.011 · Zbl 1061.65040 · doi:10.1016/j.amc.2003.08.011
[26] DOI: 10.1016/j.physleta.2005.10.005 · Zbl 1195.65207 · doi:10.1016/j.physleta.2005.10.005
[27] DOI: 10.1515/IJNSNS.2005.6.2.207 · Zbl 1401.65085 · doi:10.1515/IJNSNS.2005.6.2.207
[28] DOI: 10.1016/S0045-7825(99)00018-3 · Zbl 0956.70017 · doi:10.1016/S0045-7825(99)00018-3
[29] DOI: 10.1142/S0217979206034819 · doi:10.1142/S0217979206034819
[30] DOI: 10.1142/S0217979206033796 · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[31] DOI: 10.1016/S0096-3003(01)00312-5 · Zbl 1030.34013 · doi:10.1016/S0096-3003(01)00312-5
[32] DOI: 10.1016/j.cam.2006.09.001 · Zbl 1387.65110 · doi:10.1016/j.cam.2006.09.001
[33] DOI: 10.1016/j.amc.2006.11.179 · Zbl 1122.65388 · doi:10.1016/j.amc.2006.11.179
[34] Biazar J, Int. J. Nonlinear Sci. Numer. Simul. 8 pp 413– (2007) · Zbl 06942287 · doi:10.1515/IJNSNS.2007.8.3.413
[35] Sadighi A, Int. J. Non-linear Sci. Numer. Simul. 8 pp 435– (2007) · Zbl 06942290 · doi:10.1515/IJNSNS.2007.8.3.435
[36] Tari H, Int. J. Nonlinear Sci. Numer. Simul. 8 pp 203– (2007) · Zbl 06942263 · doi:10.1515/IJNSNS.2007.8.2.203
[37] Zayed EME, Commu. Appl. Nonlinear Anal. 15 pp 57– (2008)
[38] Zayed EME, Z. Naturforsch. 63 pp 627– (2008)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.