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- Title
New study of (3+1)-dimensional nonlinear evolution equation with main part mKdV equation and novel solitary wave solutions.
- Authors
Benoudina, Nardjess; Zhang, Wenyun; Zhang, Yi; Wazwaz, Abdul-Majid
- Abstract
Abundant hybrid solitary wave solutions have been investigated for the (3 + 1) -dimensional nonlinear evolution equation with main part mKdV equation (NLEE-mKdV) in its first study via the Lie symmetry method. The latter has been harnessed to attain 10-dimensional vector fields of symmetries from the converted NLEE-mKdV to a simpler equation under special transformation. From the derived symmetries, the corresponding one-dimensional optimal system has been constructed. Furthermore, the converted NLEE-mKdV is reduced via five subalgebras of symmetries to obtain nine novel solutions, which are shifted by the considered transformation to reach NLEE-mKdV' solutions that possess different dynamics depending on a special ansatz in adjusting the arbitrary functions and parameters. Therefore, many significant solitary wave patterns are achieved. For example, dark, bright, periodic, dipole, damped periodic, breather, kink, and their interactions are well depicted in 3D and contour plots. Most importantly, a fascinating solitary wave solution is first explored; the intrinsic insight appears on the periodically-parabolic-periodic background, which is collided with a bright soliton solution to induce a parabolic-humps breather on its top.
- Subjects
NONLINEAR evolution equations; VECTOR fields; EQUATIONS; ARBITRARY constants
- Publication
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2024, Vol 38, Issue 22, p1
- ISSN
0217-9792
- Publication type
Article
- DOI
10.1142/S021797922450293X