zbMATH — the first resource for mathematics

The extended \(F\)-expansion method and its application for a class of nonlinear evolution equations. (English) Zbl 1138.35385
Summary: By means of a simple transformation technique, we have shown that the higher-order nonlinear Schrödinger equation in nonlinear optical fibers, a new Hamiltonian amplitude equation, generalized Hirota-Satsuma coupled system and generalized ZK-BBM equation can be reduced to an elliptic-like equation. Then, the extended \(F\)-expansion method is used to obtain a series of solutions including the single and the combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear evolution equations.

35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
35C05 Solutions to PDEs in closed form
35A20 Analyticity in context of PDEs
Full Text: DOI
[1] Hirota, R., Phys rev lett, 27, 1192, (1971)
[2] Wadati, M.; Sanuki, H.; Konno, K., Prog theor phys, 53, 419, (1975)
[3] Konno, K.; Wadati, M., Prog theor phys, 53, 1652, (1975)
[4] Matveev, V.A.; Salle, M.A., Darboux transformation and solutions, (1991), Berlin Springer · Zbl 0744.35045
[5] Cariello, F.; Tabor, M., Physica D, 39, 77, (1989)
[6] Wang, M.L., Phys lett A, 199, 169, (1995)
[7] Liu, J.; Yang, L.; Yang, K., Phys lett A, 325, 268, (2004)
[8] El-Wakil, S.A.; Labany, S.K.; Zahran, M.A.; Sabry, R., Phys lett A, 299, 179, (2002)
[9] El-Wakil, S.A.; Labany, S.K.; Zahran, M.A.; Sabry, R., Appl math comput, 161, 403, (2005)
[10] Liu, J.; Yang, K., Chaos, solitons & fractals, 22, 111, (2004)
[11] Wang, M.; Li, X., Chaos, solitons & fractals, 24, 1257, (2005)
[12] Yan, Z., Chaos, solitons & fractals, 15, 575, (2003)
[13] Khater, A.H.; Hassan, M.M.; Temsah, R.S., J phys soc jpn, 74, 1431, (2005)
[14] Yomba, E., Chaos, solitons & fractals, 27, 187, (2006)
[15] Liu, C., Chaos, solitons & fractals, 23, 949, (2005)
[16] Wadati, M.; Segur, H.; Ablowitz, M.J., J phys soc jpn, 61, 1187, (1992)
[17] Wazwaz, A.M., Appl math comput, 169, 713, (2005)
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.