The (3+1)-dimensional Wazwaz-KdV equations: the conservation laws and exact solutions


Akbulut A., Rezazadeh H., Hashemi M. S. , TAŞCAN F.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1515/ijnsns-2021-0161
  • Journal Name: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: (3+1)-dimensional modified Wazwaz-KdV equations, auxiliary method, exact solutions, new conservation theorem, 02, 30 Jr, 02, 70 Wz, 94, 05 Fg, 11, 30, -j, PARTIAL-DIFFERENTIAL-EQUATIONS, LIE SYMMETRY ANALYSIS, INVARIANT SOLUTIONS, SOLITON-SOLUTIONS, OPTICAL SOLITONS, EVOLUTION

Abstract

In this study, we dealt with the new conservation theorem and the auxiliary method. We have applied the theorem and method to (3 + 1)-dimensional modified Wazwaz-KdV equations. When we applied a new conservation theorem to given equations, the obtained conservation laws did not satisfy the divergence condition. So, we modified the obtained conservation laws. These conservation laws contain extra terms. Finally, we applied the auxiliary method to given equations. We obtained two solution families with six exact solutions. All the obtained solutions are different from each other. For a suitable value of the solutions, the 3D and 2D surfaces have been plotted by Maple.