N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

Abstract

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

“…By inserting equation (19) and equation (20) into equation (5), the two soliton solutions are attained as follows:…”

“…Many scholars have explored various nonlinear frameworks in previous studies to comprehend the dynamics of solitons. Noteworthy among these models are the Schrödinger equation [18], Yu-Toda-Sasa-Fukuyama (YTSF) model [19], Fokas-Lenells model [20], Oskolkov model [21], Kadomtsev-Petviashvili (KP) model [22], and Sakovich equation [23].…”

The New Solitary Solutions to the Time-Fractional Coupled Jaulent–Miodek Equation

“…e Lie symmetry analysis has been performed on a coupled system of nonlinear timefractional Jaulent-Miodek equations associated with energydependent Schrödinger potential to find the exact solution using Erdelyi-Kober fractional derivatives [31]. Moreover, the authors of [32][33][34] obtained new exact solutions for some of PDEs using the Hirota bilinear method. e foremost objective in this article is discovering some periodic, soliton, singular, and singular-kink solutions by using two methods, namely, tan(θ/2)-expansion method and modified exp(− θ(ξ))-expansion method [35], for the time-fractional coupled JM equations.…”

Symmetry Solutions and Conservation Laws for the 3D Generalized Potential Yu-Toda-Sasa-Fukuyama Equation of Mathematical Physics

“…N-soliton solutions were derived for (1) by using bilinear transformation that included period soliton, line soliton, lump soliton, and their interaction. Moreover, for some solutions their images were drawn and their dynamic behavior was discussed in [36]. The authors of [37] invoked the extended homoclininc test and Hirota bilinear method and constructed a class of lump solutions of (1).…”