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Journal of Mathematical Physics / Volume 50 / Issue 2 / METHODS OF MATHEMATICAL PHYSICS

J. Math. Phys. 50, 023510 (2009); http://dx.doi.org/10.1063/1.3077223 (10 pages)

Homotopy perturbation method to obtain exact special solutions with solitary patterns for Boussinesq-like B(m,n) equations with fully nonlinear dispersion

Ahmet Yıldırım

Department of Mathematics, Science Faculty, Ege University, 35100 Bornova-İzmir, Turkey

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(Received 19 November 2008; accepted 5 January 2009; published online 13 February 2009)

In this paper, we studied the Boussinesq-like equations with fully nonlinear dispersion B(m,n) equations which exhibit solutions with solitary patterns. New exact solitary solutions of the equations are found. The two special cases, B(2,2) and B(3,3), are chosen to illustrate the concrete scheme of the homotopy perturbation method in B(m,n) equations. The nonlinear equations B(m,n) are addressed for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of B(m,n) equations are established.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. BASIC IDEAS OF HPM
  3. APPLICATIONS
  4. MORE EXACT SOLUTIONS
    1. The B(2,2) type
    2. The B(3,3) type
  5. GENERAL SOLUTIONS FOR B(m,n)
    1. The B(m,n) , m = n being integer
    2. The B(m,n) , m = n being odd integer
  6. CONCLUSION

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KEYWORDS and PACS

Keywords

dispersion (wave), nonlinear equations, perturbation theory, solitons

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3077223

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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