Lumps and interactions, fission and fusion phenomena in multi solitons of extended Shallow Water Wave Equation of (2+1)-dimensions

Alsufi, Nizar Abdallah; Fatima, Nahid; Noor, Adeeb; Gorji, M.R.; Alam, Mohammad Mahtab

doi:10.1016/j.chaos.2023.113410

Cited by 5 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For larger N, the dynamic behavior of the corresponding solutions is similar to remark (1-4), which is more complicated and interesting. In this paper, the amplitudes of these breather solutions decay with time, which is different from the usual breather solutions in [46,47,52].…”

Section: Yt Xxxy XX Xy Xymentioning

confidence: 68%

“…12, the line RW disappears in the periodic background without a trace. The line RW solutions in this paper are nonlocalized in space, unlike the lump wave in [47,52,53], which is localized in both time and space.…”

Section: W X Y T a Y Y A A B A Bmentioning

confidence: 90%

“…It is apparent that soliton solutions sits on the soliton or periodic line wave backgrounds when * * p p q , (36), respectively (see figures 1(c), (d)). Compared to the soliton solutions on the constant background plane in [40,46,47], these corresponding soliton solutions in this paper sit on a non-flat constant background plane.…”

Section: Yt Xxxy XX Xy Xymentioning

confidence: 99%

“…For arbitrary N = 2n, the n − line RW solutions on different backgrounds are retrieved by using theorem 1. However, the higher-order rational-type solutions of the (2 + 1)-d SWW equation cannot be constructed using a symbolic calculation approach [47,52,53]. For example, letting…”

Section: Dynamics Of Multi-line Rws On Soliton or Periodic Line Waves...mentioning

confidence: 99%

“…So far, different aspects of this equation have been investigated. For example, multi-soliton [40,46,47], oneperiodic wave solution [48][49][50], Lax pair, infinite conservation laws [51], and lump solution [47,52,53] of the equation (1) are derived. To the best of our knowledge, line rogue wave (RW) solutions of equation (1) have not been presented yet.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multiple localized waves to the (2+1)-dimensional shallow water waveequation on non-flat constant backgrounds and their applications

Cao,

Tian,

Ghanbari

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, a new general bilinear Backlund transformation and Lax pair for the (2+1)-dimensional shallow water wave equation are given in terms of the binary Bell polynomials. Based on this transformation along with introducing an arbitrary function, the multi-kink soliton, line breather, and multi-line rogue wave solutions on a non-flat constant background plane are derived. Further, we foundthat the dynamic pattern of line breather on the background of periodic line waves are similar to the two-periodic wave solutions obtained through a multi-dimensional Riemann theta function. Also, the generation mechanism and smooth conditions of the line rogue waves on the periodic line wave background are presented with longwave limit method. Additionally, a family of new rational solutions, consisting of line rogue waves and line solitons, are derived, which have never been reported before. Furthermore, the present work can be directly applied to other nonlinear equations.

show abstract

Section: Yt Xxxy XX Xy Xymentioning

confidence: 68%

Section: W X Y T a Y Y A A B A Bmentioning

confidence: 90%