Korteweg de-Vries (K-dV) has wide applications in physics, engineering and fluid mechanics. In this the Korteweg de-Vries equation with traveling solitary waves and numerical estimation of analytic solutions have been studied. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by PANG, BIAN and CHAO. We have solved the set of exact traveling wave solution analytically. Some numerical results of time dependent wave solutions have been presented graphically and discussed. This procedure has a potential to be used in more complex system of many types of K-dV equation.
 F. L. Qu and W. Q. Wang, “Alternating Segment Explicit—Implicit Scheme for Nonlinear Third-Order KdV Equation,” Applied Mathematics and Mechanics, Vol. 28, No. 7, 2007, pp. 973-980. doi:10.1007/s10483-007-0714-y
 V. A. Rukavishnikov and O. P. Tkachenko, “The Korteweg-de Vries Equation in a Cylindrical Pipe,” Computational Mathematics and Mathematical Physics, Vol. 48, No. 1, 2008, pp. 139-146. doi:10.1134/S0965542508010107
 J. Pang, C.-Q. Bian and L. Chao, “A New Auxiliary Equation Method for Finding Traveling Wave Solution to K-dV Equation,” Applied Mathematics and Mechanics (English Edition), Vol. 31, No. 7, 2010, pp. 929-936.