The Kundu–Eckhaus equation and its discretizations
نویسنده
چکیده
In this article we show that the complex Burgers and the Kundu– Eckhaus equations are related by a Miura transformation. We use this relation to discretize the Kundu–Eckhaus equation.
منابع مشابه
Exact travelling wave solutions for some complex nonlinear partial differential equations
This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion ethod for constructing exact travelling wave solutions of nonlinear partial differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and Derivat...
متن کاملApplication of the tan(phi/2)-expansion method for solving some partial differential equations
In this paper, the improved -expansion method is proposed to solve the Kundu–Eckhaus equation and Gerdjikov–Ivanov model. The applied method are analytical methods to obtaining the exact solutions of nonlinear equations. Here, the aforementioned methods are used for constructing the soliton, periodic, rational, singular and solitary wave solutions for solving some equations. We obtained furthe...
متن کاملThe Laplace-Adomian Decomposition Method Applied to the Kundu-Eckhaus Equation
The Kundu-Eckhaus equation is a nonlinear partial differential equation which seems in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics. In spite of its importance, exact solution to this nonlinear equation are rarely found in literature. In this work, we solve this equation and present a new approach to obtain the solution by means of the combined use of t...
متن کاملRogue waves of the Kundu-Eckhaus equation in a chaotic wave field.
In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plan...
متن کاملThe Modified Tanh Method for Solving the Improved Eckhausequation and the (2+1)-dimensional Improved Eckhaus Equation
The modified tanh method is one of most direct and effective algebraic method for obtaining exact solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones. In this paper,we look for exact soliton solutions of the improved Eckhaus equation and the (2+1)-dimensional improved Eckhaus equation. 2000 Mathematics Subject...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009