Periodic, Cross-Kink, and Interaction between Stripe and Periodic Wave Solutions for Generalized Hietarinta Equation: Prospects for Applications in Environmental Engineering

Abstract

In the current work, the modified (2 + 1)-dimensional Hietarinta model is considered by employing Hirota’s bilinear scheme. Likewise, the bilinear formalism is obtained for the considered model. In addition, the periodic-solitary, periodic wave, cross-kink wave, and interaction between stripe and periodic wave solutions of the mentioned equation by particular coefficients are offered. The obtained results may be used in the description of the model in fruitful way. Finally, by using the available situations, the physical demeanor of solutions is discussed in the given method. We demonstrated that these solutions validated the program using Maple and found them correct. Moreover, a lot of graphs in some sections to determine the analysis of obtained findings for the aforementioned equation are given. The achieved solutions are also verified by using the Maple software. These periodic wave solutions suggest that these three methods are useful, easy to use, and effective than other methods.

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

“…Other exact solutions such as line rogue wave [39], periodic, cross-kink, and interaction solutions between stripe and periodic wave [40] have been found. Through numerical simulation, the dynamic characteristics of different types of traveling waves have been analyzed in detail [40].…”

“…In this paper, we will study a novel (2+1)-dimensional extension of Hietarinta equation [38][39][40] as The lump solutions have been obtained via symbolic computation [38,39]. Other exact solutions such as line rogue wave [39], periodic, cross-kink, and interaction solutions between stripe and periodic wave [40] have been found. Through numerical simulation, the dynamic characteristics of different types of traveling waves have been analyzed in detail [40].…”