Lie-Backlund Symmetry Analysis and New Explicit Traveling Wave Solutions to the Generalized (2 + 1)-Dimensional Kundu-Mukherjee-Naskar Equation

Abstract

Conservation laws act as a validation tool for the correctness and physical relevance of nonlinear models. Their presence ensures that the model preserves essential physical quantities such as energy, momentum, or mass during evolution, which is especially important in realistic and applied systems. In this work, the generalized $(2+1)$-dimensional Kundu-Mukherjee-Naskar equation is comprehensively investigated. First, the Lie-Backlund symmetries analysis is performed to obtain the corresponding conservation laws using the sense of Ibragimov. Then, we solve explicitly the model by adapting the Riccati-Bernoulli sub-ODE method. Also, some graphical analysis is conducted to gain some physical insights. We believe that the conservation laws together with the obtained exact solutions indicate the integrability of the model, and provide important information regarding its dynamical behavior.