Lie symmetry reductions, exact solutions and soliton dynamics to Burgers equation

This study deals with exact solutions and soliton dynamics of Burgers equation. The Lie symmetry method under one parameter transformation is employed to establish symmetry condition, infinitesimals and their commutative relations. In consequence, the similarity variables are derived and cause to first symmetry reduction. A twice employment of method allows further symmetry reductions of test equations and results to systems of ODEs. Then, the ODEs have been integrated under parametric constraints and evolve desired exact solutions. These solutions consist of all the functions \(f_1(t)\) $f_1(t)$ , \(f_2(t)\) $f_2(t)$ , \(g_1(y)\) $g_1(y)$ , \(g_2(y)\) $g_2(y)$ existed in infinitesimals, more arbitrary functions F(X), H(X) and several arbitrary constants that make obtained results generalize than previous findings. To analyze the nature of physical phenomena associated with Burgers equation, these solutions have been supplemented with numerical simulation. Consequently, single soliton, doubly soliton, multisoliton, asymptotic nature, soliton fusion and fission nature are discussed systematically. Moreover, the Lagrangian formulation and conserved vectors associated with Lie symmetries are obtained.