Study of the N-Soliton Solutions of the (2+1)
Dimensional Nonlinear Wave Equation

Wuming Li; Geyao Li

doi:https://doi.org/10.14445/22315373/IJMTT-V72I1P112

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 1 | Year 2026 | Article Id. IJMTT-V72I1P112 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I1P112

Study of the N-Soliton Solutions of the (2+1) Dimensional Nonlinear Wave Equation

Wuming Li, Geyao Li

Received	Revised	Accepted	Published
28 Nov 2025	04 Jan 2026	22 Jan 2026	31 Jan 2026

Citation :

Wuming Li, Geyao Li, "Study of the N-Soliton Solutions of the (2+1) Dimensional Nonlinear Wave Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 1, pp. 167-185, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I1P112

Abstract

In this paper, a (2+1)-dimensional nonlinear wave equation is investigated using the Hirota bilinear method. The N-soliton solutions of this Equation are constructed, and the corresponding local characteristics are analyzed. By selecting specific parameters, various localized waves are derived, including kink solitons, lump solitons, periodic solitons, and so on. Furthermore, the dynamical behaviors of the soliton solutions are exhibited by using the symbolic computation system Maple, and the interaction characteristics of these solutions are elaborated through the corresponding images. Lastly, the ansatz approach is utilized to work out an interesting inelastic interaction solution where lump solitons can occur. These findings in this study are very helpful for deepening the comprehension of the interaction mechanisms exhibited by localized waves in nonlinear wave equations.

Keywords

Nonlinear Wave Equation, Hirota Bilinear Method, Soliton Solution, Lump Solution, Periodic Solution.

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