Explicit solutions of nonlinear partial differential equations. (English) Zbl 0904.35077

Summary: Explicit solutions to Burgers equation are calculated by the decomposition method for comparison with other existing procedures such as similarity reduction.


35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
Full Text: DOI


[1] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Acad. Publ · Zbl 0802.65122
[2] Cherruault, Y., Convergence of Adomian’s method, Kybernetes, 18, 2, 21-38 (1989) · Zbl 0697.65051
[4] Mavoungou, T.; Cherruault, Y., Numerical study of Fisher’s equation by Adomian’s method, Math. Comput. Modelling, 19, 1, 89-95 (1994) · Zbl 0799.65099
[5] Abbaoui, K.; Cherruault, Y., convergence of Adomian’s method applied to differential equations, Comp. Math. Applic., 28, 5, 103-109 (1994) · Zbl 0809.65073
[6] Adomian, G., The solution of general linear and nonlinear stochastic systems, (Rose, J., Modern Trends in Cybernetics and Systems (1976), Editura Technica: Editura Technica Romania) · Zbl 0426.93048
[7] Adomian, G., Nonlinear Stochastic Operator Equations (1986), Academic Press · Zbl 0614.35013
[8] Burgers, J. M., A Mathematical model illustrating the theory of turbulence, Adv. App. Mech., 1, 171-199 (1948)
[9] Hood, S., New exact solutions of Burgers’ equation—an extension to the direct method of Clarkson and Kruskal, J. Math. Phys., 36, 4, 1971-1990 (1995) · Zbl 0830.35120
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.