Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves

Abstract

• (4+1) Fokas equation - is studied. • New Lie symmetries of the Fokas equation are investigated. • Fokas equation is reduced to ODEs . • Some new exact solutions are derived. • Compare our results with other works. 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.