Abstract
The Fokas-Lenells model has broad applications in nonlinear physics when studying various soliton phenomena. Employing the direct algebraic scheme, the modified rational sine-cosine technique, and the (1/G′) expansion scheme, the analytical solutions to this model are derived. Double periodic waves, bright soliton, dark soliton, single and multiple breather waves, and periodic breather waves are extracted from this model using symbolic computation. The dynamic behaviors of the acquired outcomes are vividly illustrated through density, two-dimensional (2D), and three-dimensional (3D) graphical representations. These discoveries are strategically positioned to significantly contribute to the advancement in the exploration of nonlinear models, standing as a fundamental pillar for forthcoming research endeavors.