Similarity Solutions of Shallow Water Wave Equation

The marine biodiversity, solid state physics and study on plasma physics, fluid flows have been represented by the shallow water wave equations. The proposed technique is convenient flexible and acts as a powerful tool to find the accurate solutions of the PDEs. The Symmetry Analysis plays a dominant role in construction of perfect solutions to nonlinear PDE. A nonlinear PDE has vast applications in real life. The solution of Nonlinear PDE using symmetric Analysis is a challenging work. In this paper the Lie group of infinitesimal transformation is used to apply the theory of classical method to the perturbed shallow water wave equation. The case studies and the discussion of the group of theoretic techniques of classical symmetry and Painleve's analysis either strongly or collectively as the case may be for obtaining solutions of the perturbed shallow water wave equation are revealed. These GSWW have a wide range of applications in the field of oceanography, atmospheric pressure and marine environment.