Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method
نویسندگان
چکیده
Applications in physics are modeled by nonlinear systems. Very few nonlinear systems have closed form solutions, therefore, many researchers stress their goals to search numerical solutions. Homotopy analysis method HAM , first proposed by Liao 1 , is an elegant method which has proved its effectiveness and efficiency in solving many types of nonlinear equations 2, 3 . Liao in his book 4 proved that HAM is a generalization of some previously used techniques such as the d-expansion method, artificial small parameter method 5 , and Adomian decomposition method. Moreover, unlike previous analytic techniques, the HAM provides a convenient way to adjust and control the region and rate of convergence 6 . Recently, new interested applications of the homotopy analysis have been introduced by Abbasbandy and coauthors 7, 8 . Also, in 9 HAM is used to study the effects of thermocapillarity and thermal radiation on flow and heat transfer in a thin liquid film. In this work, we consider a two-component evolutionary system of a homogeneous KdV equations of third order type I and II given, respectively, by
منابع مشابه
Approximate Solutions to System of Nonlinear Partial Differential Equations Using Homotopy Perturbation Method
Abstract: In this paper, the homotopy perturbation method (HPM) is applied to obtain approximate solutions to three systems of nonlinear wave equations, namely, two component evolutionary system of a homogeneous KdV equations of order 3 (type I) as well as (type II), and the generalized coupled Hirota Satsuma KdV. The numerical results show that this method is a powerful tool for solving system...
متن کاملNew analytical soliton type solutions for double layers structure model of extended KdV equation
In this present study the double layers structure model of extended Korteweg-de Vries(K-dV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma model. Then by using of new analytical method we obtain the new exact solitary wave solutions of this equation. Double layer is a structure in plasma and consists of two p...
متن کاملOn The Simulation of Partial Differential Equations Using the Hybrid of Fourier Transform and Homotopy Perturbation Method
In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...
متن کاملHomotopy Analysis Method for Solving Kdv Equations
A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement.
متن کاملNumerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method
In this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax'sseven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so-lutions and numerical solutions of the sSK and LsKdV equations for the initialconditions. The numerical solutions are compared with the known analyticalsolutions. Their remarkabl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012