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Exact solutions for the fourth order nonlinear Schrödinger equations with cubic and power law nonlinearities. (English) Zbl 1136.35458

Summary: The tanh method and the sine-cosine method are used to solve the fourth order nonlinear Schrödinger equations with cubic and power law nonlinearities. Several exact solutions with distinct structures are formally obtained for each type of nonlinearity. The results confirm the applicability of these two methods in handling nonlinear problems

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C05 Solutions to PDEs in closed form
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[1] Bang, O.; Christiansen, P.L.; If, F.; Rasmussen, K., White noise in the two-dimensional nonlinear schrodinger equation, Appl. anal., 57, 3-15, (1995) · Zbl 0842.35111
[2] Liu, S.; Fu, Z.; Liu, Sh.; Wang, Z., Stationary periodic solutions and asymptotic series solutions to nonlinear evolution equations, Chinese J. phys., 42, 2, 127-134, (2004)
[3] Ablowitz, M.; Segur, H., Solitons and the inverse scattering transform, (1981), SIAM Philadelphia · Zbl 0472.35002
[4] Hirota, R., Direct methods in soliton theory, (1980), Springer Berlin
[5] Lax, P.D., Periodic solutions of the Korteweg-de Vries equation, Comm. pure. appl. math., 28, 141-188, (1975) · Zbl 0295.35004
[6] Malfliet, W., Solitary wave solutions of nonlinear wave equations, Amer. J. phys., 60, 7, 650-654, (1992) · Zbl 1219.35246
[7] Malfliet, W., The tanh method:I. exact solutions of nonlinear evolution and wave equations, Phys. scripta, 54, 563-568, (1996) · Zbl 0942.35034
[8] Malfliet, W., The tanh method:II. perturbation technique for conservative systems, Phys. scripta, 54, 569-575, (1996) · Zbl 0942.35035
[9] Wazwaz, A.M., The tanh method for travelling wave solutions of nonlinear equations, Appl. math. comput., 154, 3, 713-723, (2004) · Zbl 1054.65106
[10] Wazwaz, A.M., Partial differential equations: methods and applications, (2002), Balkema Publishers The Netherlands · Zbl 0997.35083
[11] Wazwaz, A.M., A reliable technique for solving linear and nonlinear schrodinger equations by Adomian decomposition method, Bull. inst. math. acad. sinica, 29, 2, 125-134, (2001) · Zbl 1005.35007
[12] Wazwaz, A.M., A study on nonlinear dispersive partial differential equations of compact and noncompact solutions, Appl. math. comput., 135, 2-3, 399-409, (2003) · Zbl 1027.35120
[13] Wazwaz, A.M., A construction of compact and noncompact solutions of nonlinear dispersive equations of even order, Appl. math. comput., 135, 2-3, 311-324, (2003)
[14] Wazwaz, A.M., Compactons in a class of nonlinear dispersive equations, Math. comput. modelling, 37, 3-4, 333-341, (2003) · Zbl 1044.35078
[15] Wazwaz, A.M., Distinct variants of the KdV equation with compact and noncompact structures, Appl. math. comput., 150, 365-377, (2004) · Zbl 1039.35110
[16] Wazwaz, A.M., Variants of the generalized KdV equation with compact and noncompact structures, Comput. math. appl., 47, 583-591, (2004) · Zbl 1062.35120
[17] Wazwaz, A.M., New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations, Chaos solitons fractals, 22, 249-260, (2004) · Zbl 1062.35121
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