THE EXACT SOLUTION OF KLEIN-GORDON'S EQUATION BY FORMAL LINEARIZATION METHOD

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 4,  2008, pp.631-635
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.4.631
Title & Authors
THE EXACT SOLUTION OF KLEIN-GORDON'S EQUATION BY FORMAL LINEARIZATION METHOD

Abstract
In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $\small{u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+}$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.
Keywords
Formal linearization;Klein-Gordon's equation;non-linear partial differential equations;
Language
English
Cited by
1.
Exact multisoliton solutions of nonlinear Klein-Gordon equation in 1 + 2 dimensions, The European Physical Journal Plus, 2013, 128, 11
2.
THE FORMAL LINEARIZATION METHOD TO MULTISOLITON SOLUTIONS FOR THREE MODEL EQUATIONS OF SHALLOW WATER WAVES, Journal of the Chungcheong Mathematical Society , 2012, 25, 3, 381
References
1.
Rosales R.R., Exact solutions of some nonlinear evolution equations, Studies Appl. Math., 59 (1978), pp. 117-151.

2.
Baikov V.A.,Gazizov R.K. and Ibragimov N.H., Linearization and formal symmetries of the Korteweg-de Vries equation, Dokl. Akad. Nauk SSSR, 303, No. 4(1989), pp. 781-784.

3.
Bobylev A.V.,Structure of general solution and classification of particular solutions of the nonlinear Boltzmann equation for Maxwell molecules,DokI.Akad.Nauk SSSR, 251, No.6 (1980), pp. 1361-1365.

4.
Bobylev A.V.,Poincare theorem,Boltzmann equation and Korteweg-de Vries type equations. Dokl.Akad. Nauk SSSR, 256 No. 6 (1981), pp. 1341-1346.

5.
Bobylev A.V., Exact solutions of the nonlinear Boltzmann equations and the theory of relaxation of t he Maxwell gas,Teor.Mat.Fiz., 60, No. 2 (1984), pp. 280-310.

6.
Vedenyapin V.V., Anisotropic solutions of the nonliear Boltzmann equation for Maxwell Molecules, Dokl. Akad. Nauk SSSR, 256, No. 2 (1981), pp. 338-342.

7.
Vedenyapin V.V., Differential forms in spaces without norm. Theorem about Boltzmann H-function uniqueness, Usp. Mat. Nauk, 43, No. 1 (1988), pp. 159-179.

8.
Mishchenko A.V. and Petrina D.Ya., Linearization and exact solutions for a class of Boltzmann equations, Teor. Mat. Fiz., 77, No. 1 (1988), pp. 135-153.

9.
Nikolenko N.V., Invariant, asymptoticaily stable torus of perturbed Korteweg-de Vries equation, Usp. Mat. Nauk, 35, No. 5 (1980), pp. 121-180.

10.
Dobrohotov S.Yu. and Muslov V.P.,Many-dimensional Dirichlet series in the problem of asymptotics of nonlinear elliptic operators spectral series, In: Modern problems of Mathematics, 23 (1983), Moscow (in Russian).