Analytic solutions and conservation laws of a (2+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama equation

Abstract This article analytically investigates a (2+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama equation. We secure the solutions of this equation via the engagement of Lie symmetry reductions alongside direct integration techniques. We gain non-topological 1-soliton as well as periodic function solutions of the equation. Series solution of the underlying equation is also achieved by exploiting power series technique. Furthermore, the utilization of ( G ′ / G ) -expansion method is done in procuring some closed-form solutions of the equation. Graphical exhibition of the dynamical character of the gained results is given in a bid to have a sound understanding of the physical phenomena of the underlying model. Conclusively, we give the conserved vectors of the aforementioned equation by employing both the standard multiplier approach as well as the Ibragimov’s conservation theorem.