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The multisoliton solution of generalized Burger's equation by the formal linearization method

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초록

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.

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.

참고문헌 (10)

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  2. V. A. Baikov, "Poincare's theorem. Boltzmann's equation and Korteweg-de Vries-type equa- tions", Dokl. Akad. Nauk SSSR, 256(6), pp.1341~1346 (1981)
  3. V. A. Baikov, "Exact solutions of the nonlinear Boltzmann equation and the theory of relax- ation of a Maxwell gas", Teoret. Mat. Fiz, 60(2), pp.280~310 (1984)
  4. V. A. Baikov, "Linearization and formal sym- metries of the Korteweg-de Vries equation", Dokl. Akad. Nauk SSSR, 38(3), pp.588~591 (1988)
  5. A. V. Mishchenko, "Linearization and exact solutions of a class of Boltzmann equations", Teoret. Mat. Fiz, 77(1), pp.135~153 (1988)
  6. N. V. Nikolenko, "Invariant, asymptotically stable tori of the perturbed Korteweg-de Vries equation", Uspekhi Mat. Nauk, 35(5), pp.121~272 (1980)
  7. R. R. Rosales, "Exact solutions of some nonlinear evolution equations", Stud. Appl. Math, 59(2), pp.117~151 (1978)
  8. V. V. Vedenyapin, "Anisotropic solutions of a nonlinear Boltzmann equation for Maxwell molecules", Dokl. Akad. Nauk SSSR, 256(2), pp.338~342 (1981)
  9. V. V. Vedenyapin, "Differential forms in spaces without a norm. A uniqueness theorem for the Boltzmann H-function", Uspekhi Mat. Nauk, 43(1), pp.193~219 (1988), trans- lation in Russian Math. Surveys
  10. V. V. Vedenyapin, "Exponential series and superposition of travelling waves"

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