Abstract
In this paper, the homotopy analysis method (HAM) proposed by Liao is adopted for solving Davey–Stewartson (DS) equations which arise as higher dimensional generalizations of the nonlinear Schrödinger (NLS) equation. The results obtained by HAM have been compared with the exact solutions and homotopy perturbation method (HPM) to show the accuracy of the method. Comparisons indicate that there is a very good agreement between the HAM solutions and the exact solutions in terms of accuracy.
Highlights
Partial differential equations which arise in real-world physical problems are often too complicated to be solved exactly
The homotopy analysis method has been successfully applied to finding the solution of Davey–Stewartson equations
The solution obtained by the homotopy analysis method is an infinite power series for appropriate initial condition, which can, in turn, be expressed in a closed form, the exact solution
Summary
Partial differential equations which arise in real-world physical problems are often too complicated to be solved exactly. The Davey–Stewartson I and II are two well-known examples of integrable equations in two space dimensions, which arise as higher dimensional generalizations of the nonlinear Schrodinger (NLS) equation [4]. They appear in many applications, for example in the description of gravity-capillarity surface wave packets in the limit of the shallow water. Alipour (HAM), [5,6,7,8,9,10,11] This method has been successfully applied to solve many types of nonlinear problems [12,13,14,15,16,17,18]. We will apply homotopy analysis method to the problem mentioned above
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