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A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations. (English) Zbl 1070.65102
Summary: We consider coupled higher-dimensional Burgers equations. We find periodic solutions to these equations using a modified Adomian’s decomposition method. We find both exact and numerical solutions. We compare the numerical solutions with corresponding analytical solutions. We also show the effectiveness of the method.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
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Full Text: DOI
References:
[1] Cross, M. C.; Hohenberg, P. C.: Pattern formation outside of equilibrium. Rev. mod. Phys. 65, 851-1112 (1993)
[2] Ablowitz, M. J.; Clarkson, P. A.: Solitons, nonlinear evolution equations and inverse scattering. (1991) · Zbl 0762.35001
[3] Rogers, C.; Shadwich, W. F.: Bäcklund transformations and their application. (1982)
[4] Olver, P. J.: Applications of Lie groups to differential equations. (1986) · Zbl 0588.22001
[5] Adomian, G.: A review of the decomposition method in applied mathematics. J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053
[6] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[7] Dehghan, M.: The use of Adomian decomposition method for solving the one-dimensional parabolic equation with non-local boundary specifications. Int. J. Comput. math. 81, 25-34 (2004) · Zbl 1047.65089
[8] Cherruault, Y.: Optimisation methodes locales et globales. (1999)
[9] Kaya, D.: On the solution of a Korteweg-de Vries like equation by the decomposition method. Int. J. Comput. math. 72, 531-539 (1999) · Zbl 0948.65104
[10] Kaya, D.; El-Sayed, S. M.: On the solution of the coupled Schrödinger-KdV equation by the decomposition method. Phys. lett. A 313, 82-88 (2003) · Zbl 1040.35099
[11] Kaya, D.: Solitary wave solutions for a generalized Hirota-satsuma coupled KdV equation. Appl. math. Comput. 147, 69-78 (2004) · Zbl 1037.35069
[12] Kaya, D.; Inan, I. E.: Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation. Appl. math. Comput. 151, 775-787 (2004) · Zbl 1048.65096
[13] Seng, V.; Abbaoui, K.; Cherruault, Y.: Adomian’s polynomials for nonlinear operators. Math. comput. Modell. 24, 59-65 (1996) · Zbl 0855.47041
[14] Wazwaz, A. M.: A computational approach to soliton solutions of the Kadomtsev-petviashili equation. Appl. math. Comput. 123, 205-217 (2001) · Zbl 1024.65098
[15] Wazwaz, A. M.: Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Chaos, solitons & fractals 12, 1549-1556 (2001) · Zbl 1022.35051
[16] Wazwaz, A. M.: Partial differential equations: methods and applications. (2002) · Zbl 1079.35001
[17] Salerna, M.: On the phase manifold geometry of the two-dimensional Burgers equations. Phys. lett. A 121, 15-18 (1987)
[18] Lu, Z.; Zhang, H.: New applications of a further extended tanh method. Phys. lett. A 324, 293-298 (2004) · Zbl 1123.35350
[19] Kaya, D.: An application of the decomposition method on second order wave equations. Int. J. Comput. math. 75, 235-245 (2000) · Zbl 0964.65113
[20] Wazwaz, A. M.: A study of nonlinear dispersive equations with solitary-wave solutions having compact support. Math. comput. Simul. 56, 269-276 (2001) · Zbl 0999.65109
[21] Kaya, D.: The use of Adomian decomposition method for solving a specific non-linear partial differential equations. Bull. belg. Math. soc. 9, 343-349 (2002) · Zbl 1038.35093
[22] Kaya, D.; Yokus, A.: A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations. Math. comput. Simul. 60, 507-512 (2002) · Zbl 1007.65078
[23] Kaya, D.: An explicit and numerical solutions of some fifth-order KdV equation by decomposition method. Appl. math. Comput. 144, 353-363 (2003) · Zbl 1024.65096
[24] Shawagfeh, N.; Kaya, D.: Comparing numerical methods for the solutions of system of ordinary differential equations. Appl. math. Lett. 17, 323-328 (2004) · Zbl 1061.65062