Abstract
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.
Highlights
We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by PANG, BIAN and CHAO
We are interested in trying our scheme for the wave solution of the Korteweg de-Vries (K-dV) equation
It is found that there are nine exact traveling wave solutions (12)-(20) of 2-dimentional K-dV equation exist for real sense depends on different relevant physical parameters but the last one is exact the same as (20)
Summary
The resulting asymptotic expressions in the radial coordinate differ considerably from the classical expansion in depth for shallow-water waves, they are able to derive the Kd-V equation. They show how to proceed back from the Kd-V equation to the velocity function and present the numerical results obtained for a model problem. Al-Jamal studied the boundary control problem of the generalized Korteweg-de Vries Burger (GKdVB) equation on the interval [0,1], [6]. They presented a numerical results supporting the analytical ones for both the controlled and uncontrolled equations using a finite element method
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