Browse > Article
http://dx.doi.org/10.4134/CKMS.2011.26.2.207

THE MULTISOLITON SOLUTION OF GENERALIZED BURGER'S EQUATION BY THE FORMAL LINEARIZATION METHOD  

Mirzazadeh, Mohammad (Department of Mathematics Faculty of Science, University of Guilan)
Taghizadeh, Nasir (Department of Mathematics Faculty of Science, University of Guilan)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.2, 2011 , pp. 207-214 More about this Journal
Abstract
The formal linearization method is an efficient method for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, we obtain multisoliton solution of generalization Burger's equation and the (3+1)-dimension Burger's equation and the Boussinesq equation by the formal linearization method.
Keywords
formal linearization method; multisoliton solution; generalized Burger's equation; (3 + 1)-dimension Burger's equation; Boussinesq equation;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 R. R. Rosales, Exact solutions of some nonlinear evolution equations, Stud. Appl. Math. 59 (1978), no. 2, 117-151.   DOI
2 V. V. Vedenyapin, Anisotropic solutions of a nonlinear Boltzmann equation for Maxwell molecules, Dokl. Akad. Nauk SSSR 256 (1981), no. 2, 338-342.
3 V. V. Vedenyapin, Differential forms in spaces without a norm. A uniqueness theorem for the Boltzmann H-function, Uspekhi Mat. Nauk 43 (1988), no. 1(259), 159-179, 248
4 V. V. Vedenyapin, Differential forms in spaces without a norm. A uniqueness theorem for the Boltzmann H-function, Russian Math. Surveys 43 (1988), no. 1, 193-219.   DOI   ScienceOn
5 V. V. Vedenyapin, Exponential series and superposition of travelling waves, (to appear).
6 V. A. Baikov, Structure of the general solution and classification of partial sums of the Boltzmann nonlinear equation for Maxwellian molecules, Dokl. Akad. Nauk SSSR 251 (1980), no. 6, 1361-1365.
7 V. A. Baikov, Poincare's theorem. Boltzmann's equation and Korteweg-de Vries-type equations, Dokl. Akad. Nauk SSSR 256 (1981), no. 6, 1341-1346.
8 V. A. Baikov, Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwell gas, Teoret. Mat. Fiz. 60 (1984), no. 2, 280-310.
9 V. A. Baikov, R. K. Gazizov, and N. Kh. Ibragimov, Linearization and formal symmetries of the Korteweg-de Vries equation, Dokl. Akad. Nauk SSSR 303 (1988), no. 4, 781-784
10 V. A. Baikov, R. K. Gazizov, and N. Kh. Ibragimov, Linearization and formal sym- metries of the Korteweg-de Vries equation, Soviet Math. Dokl. 38 (1989), no. 3, 588-591.
11 N. V. Nikolenko, Invariant, asymptotically stable tori of the perturbed Korteweg-de Vries equation, Uspekhi Mat. Nauk 35 (1980), no. 5(215), 121-180, 271-272.
12 A. V. Mishchenko and D. Ya Petrina, Linearization and exact solutions of a class of Boltzmann equations, Teoret. Mat. Fiz. 77 (1988), no. 1, 135-153.