Abundant interaction between lump and k-kink, periodic and other analytical solutions for the (3+1)-D Burger system by bilinear analysis

Zhao N., Manafian J., İLHAN O. A., Singh G., Zulfugarova R.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, cilt.35, sa.13, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 13
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s0217979221501733
  • Dergi Adı: INTERNATIONAL JOURNAL OF MODERN PHYSICS B
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Lump and k-kink solutions, Hirota bilinear operator method, (3+1)-dimensional, Burger system, the bilinear form equation, PARTIAL-DIFFERENTIAL-EQUATIONS, SOLITONS, WAVES
  • Erciyes Üniversitesi Adresli: Evet

Özet

In this paper, we study the (3+1)-dimensional Burger system which is considered in soliton theory and generated by considering the Hirota bilinear operators. The bilinear frame to the Burger system by using the multi-dimensional Bell polynomials is constructed. Also, based on the binary Backlund transformations, the generalized Bell polynomials are written. We retrieve some novel exact analytical solutions, containing interaction between lump and two kink wave solutions, interaction between lump and periodic wave solutions, interaction between stripe and periodic solutions, breather wave solutions, cross-kink wave solutions, interaction between kink and periodic wave solutions, multi-wave solutions, and finally solitary wave solutions for the (3+1)-dimensional Burger system by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota trilinear forms and their generalized equivalences.