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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.

MSC:
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
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References:
[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)
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