Abstract
Using the algebraic approach Lie symmetries, we spin new infinitesimals for the (4 + 1) Fokas equation that admits an infinite number of possibilities for its Lie vectors. Through the commutation product between the unknown vectors, we generate a system of ordinary differential equations (ODEs). By solving this system, we explore these infinitesimals. Through four stages of the similarity reduction using double and triple combinations between the examined vectors, we explore new soliton solutions. These results are simulated through three and two-dimensional plots that illustrates the dynamical behavior of these solutions is presented for different values of the free valued function at different values of time. A comparison with other results is presented. (c) 2020 Elsevier Ltd. All rights reserved.