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

  • Received : 2008.10.04
  • Accepted : 2010.11.21
  • Published : 2011.04.30

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

References

  1. 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.
  2. 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.
  3. 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.
  4. 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
  5. 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.
  6. 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.
  7. 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.
  8. R. R. Rosales, Exact solutions of some nonlinear evolution equations, Stud. Appl. Math. 59 (1978), no. 2, 117-151. https://doi.org/10.1002/sapm1978592117
  9. V. V. Vedenyapin, Anisotropic solutions of a nonlinear Boltzmann equation for Maxwell molecules, Dokl. Akad. Nauk SSSR 256 (1981), no. 2, 338-342.
  10. 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
  11. 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. https://doi.org/10.1070/RM1988v043n01ABEH001528
  12. V. V. Vedenyapin, Exponential series and superposition of travelling waves, (to appear).

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  1. THE FORMAL LINEARIZATION METHOD TO MULTISOLITON SOLUTIONS FOR THREE MODEL EQUATIONS OF SHALLOW WATER WAVES vol.25, pp.3, 2012, https://doi.org/10.14403/jcms.2012.25.3.381