The decomposition method for solving (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation

El-Sayed S. M., KAYA D.

Applied Mathematics and Computation, cilt.157, sa.2, ss.523-534, 2004 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 157 Sayı: 2
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1016/j.amc.2003.08.059
  • Dergi Adı: Applied Mathematics and Computation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.523-534
  • Anahtar Kelimeler: (2 + 1)-dimensional Boussinesq equation, (3 + 1)-dimensional KP equation, Decomposition method, Numerical solutions, Solitary-wave solutions
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

We study the solitary-wave solutions of the (2+1)-dimensional Boussinesq equation utt-uxx-uyy-(u2) xx-uxxxx=0 and (3+1)-dimensional KP equation u xt-6ux2+6uuxx-u xxxx-uyy-uzz=0. In this paper by considering the decomposition scheme, we first obtain the exact solitary-wave solutions of the (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation for the initial conditions without using any classical transformations and then its numerical solutions are constructed without using any discretization technique. The numerical solutions are compared with the known analytical solutions. Its remarkable accuracy is finally demonstrated in the study of (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation. © 2003 Elsevier Inc. All rights reserved.