Multiple-soliton solutions for the generalized -dimensional and the generalized -dimensional Ito equations

Applied Mathematics and Computation - Tập 202 - Trang 840-849 - 2008
Abdul-Majid Wazwaz1
1Department of Mathematics, Saint Xavier University, Chicago, IL 60655, United States

Tài liệu tham khảo

Ito, 1980, An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order, J. Phys. Soc. Jpn., 49, 771, 10.1143/JPSJ.49.771 Li, 2007, Soliton solutions to a higher order Ito equation: Pfaffian technique, Phys. Lett. A, 363, 1, 10.1016/j.physleta.2006.10.080 Springael, 1996, Bilinear characterization of higher order Ito equation, J. Phys. Soc. Jpn., 65, 1222, 10.1143/JPSJ.65.1222 Hirota, 1974, A new form of Bäcklund transformations and its relation to the inverse scattering problem, Prog. Theor. Phys., 52, 1498, 10.1143/PTP.52.1498 Hirota, 2004 Hirota, 1971, Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27, 1192, 10.1103/PhysRevLett.27.1192 Hirota, 1972, Exact solutions of the modified Korteweg-de Vries equation for multiple collisions of solitons, J. Phys. Soc. Jpn., 33, 1456, 10.1143/JPSJ.33.1456 Hirota, 1972, Exact solutions of the Sine-Gordon equation for multiple collisions of solitons, J. Phys. Soc. Jpn., 33, 1459, 10.1143/JPSJ.33.1459 Sawada, 1974, A method for finding N-soliton solutions of the KdV equation and KdV-like equation, Prog. Theor. Phys., 51, 1355, 10.1143/PTP.51.1355 Lax, 1968, Integrals of nonlinear equations of evolution and solitary waves, Commun. Pure Appl. Math., 21, 467, 10.1002/cpa.3160210503 Matsuno, 1984 Goktas, 1999, Symbolic computation of conserved densities for systems of nonlinear evolution equations, J. Symbol. Comput., 11, 1 Hietarinta, 1987, A search for bilinear equations passing Hirota’s three-soliton condition I KdV-type bilinear equations, J. Math. Phys., 28, 1732, 10.1063/1.527815 Hietarinta, 1987, A search for bilinear equations passing Hirota’s three-soliton condition II mKdV-type bilinear equations, J. Math. Phys., 28, 2094, 10.1063/1.527421 Hereman, 1980, Symbolic software for soliton theory, Acta Appl. Math., Phys. Lett. A, 76, 95 Hereman, 1997, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. Comput. Simul., 43, 13, 10.1016/S0378-4754(96)00053-5 Weiss, 1984, On classes of integrable systems and the Painlevé property, J. Math. Phys., 25, 13, 10.1063/1.526009 Malfliet, 2004, The tanh method a tool for solving certain classes of nonlinear evolution and wave equations, J. Comput. Appl. Math., 164–165, 529, 10.1016/S0377-0427(03)00645-9 Malfliet, 1992, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60, 650, 10.1119/1.17120 Malfliet, 1996, The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Phys. Scripta, 54, 563, 10.1088/0031-8949/54/6/003 Malfliet, 1996, The tanh method: II. Perturbation technique for conservative systems, Phys. Scripta, 54, 569, 10.1088/0031-8949/54/6/004 Wazwaz, 2004, The tanh method for travelling wave solutions of nonlinear equations, Appl. Math. Comput., 154, 713, 10.1016/S0096-3003(03)00745-8 Wazwaz, 2002 Wazwaz, 2007, The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations, Appl. Math. Comput., 184, 1002, 10.1016/j.amc.2006.07.002 Wazwaz, 2007, The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations, Appl. Math. Comput., 188, 1467, 10.1016/j.amc.2006.11.013 Wazwaz, 2002, New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations, Chaos Soliton Fract., 13, 321, 10.1016/S0960-0779(00)00249-6 Wazwaz, 2007, Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method, Appl. Math. Comput., 190, 633, 10.1016/j.amc.2007.01.056 Wazwaz, 2007, The tanh–coth and the sech methods for exact solutions of the Jaulent–Miodek equation, Phys. Lett. A, 366, 85, 10.1016/j.physleta.2007.02.011 Wazwaz, 2007, Multiple-front solutions for the Burgers equation and the coupled Burgers equations, Appl. Math. Comput., 190, 1198, 10.1016/j.amc.2007.02.003 Wazwaz, 2007, Multiple-soliton solutions for the Boussinesq equation, Appl. Math. Comput., 92, 479, 10.1016/j.amc.2007.03.023