Bright-Dark Solitons, Kink Wave and Singular Periodic Wave Solutions for the Lonngren-Wave Equation (Journal of Nonlinear Modeling and Analysis, 2024)
In this article, exact solutions of the Lonngren-wave equation areinvestigated. Firstly, the equation is transformed into an ordinary differentialequation by traveling wave transformation. Based on the homogeneous balancemethod, bright-solitons and singular periodic wave solutions of the equationare derived by applying the simple function expansion method and the Riccatiequation method. Applying the $Exp(−φ(ς))$ expansion method, we constructdark-solitons and kink wave solutions of the equation. Moreover, the 3-D,2-D and density plots are drawn by choosing the appropriate parameters sothat the properties of the solutions can be better studied. According to theFigures, the analysis of the dynamical behavior of the solutions is provided.This article enriches the diversity of the solutions of the equation.