Abstract
The unidirectional propagation of long waves in certain nonlinear dispersive waves is explained by the (2 + 1) pKP equation, this equation admits infinite number of infinitesimals. We explored new Lie vectors thorough the commutative product properties. Using the Lie reduction stages and some assistant methods to solve the reduced ODEs, Exploiting a set of new solutions. Exploring a set of non-singular local multipliers; generating a set of local conservation laws for the studied equation. The nonlocally related (PDE) systems are found. Four nonlocally related systems are discussed reveal twenty-one interesting closed form solutions for this equation. We investigate new various solitons solutions as one soliton, many soliton waves move together, two and three Lump soliton solutions. Though three dimensions plots some selected solutions are plotted.