EXACT SOLUTIONS OF A CLASS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Uxt=U2N+1 WHERE N IS NON ZERO REAL RATIONAL NUMBER

Abstract

Using Lie Group Similarity Transformation, a class of nonlinear partial differential equations, u_xt = u²ⁿ⁺¹ where n is any real rational number of the form p/q where p and q are any positive or negative integers ,except n = 0 and n = −1/2 is reduced to second order nonlinear ordinary differential equation and found exact solutions . Each and every exact solution is a combination of a pair of exact distinct solutions and both exist independently. They form a new class of solutions of Klein-Gordon family of nonlinear partial differential equations.