New application to Riccati equation

doi:10.1088/1674-1056/19/8/080303

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80303-080303.doi: 10.1088/1674-1056/19/8/080303

New application to Riccati equation

李姝敏¹, 套格图桑², 斯仁道尔吉²

(1)College of Mathematical Science, Bao Tou Teachers' College, Bao Tou 014030, China; (2)College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

收稿日期:2009-09-19 修回日期:2009-12-14 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10461006), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ07031), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 200408020103) and the Natural Science Research Program of Inner Mongolia Normal University, China (Grant No. QN005023).

New application to Riccati equation

Taogetusang(套格图桑)^a)^†, Sirendaoerji(斯仁道尔吉)^a), and Li Shu-Min(李姝敏)^b)

^a College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China; ^b College of Mathematical Science, Bao Tou Teachers' College, Bao Tou 014030, China

Received:2009-09-19 Revised:2009-12-14 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10461006), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ07031), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 200408020103) and the Natural Science Research Program of Inner Mongolia Normal University, China (Grant No. QN005023).

摘要/Abstract

摘要： To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov–Kuznetsov equation, Karamoto–Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.

Abstract: To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov–Kuznetsov equation, Karamoto–Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.

Key words: Riccati equation, formula of nonlinear superposition, nonlinear evolution equation, exact solution

中图分类号: (Solitons)

05.45.Yv

02.30.Hq (Ordinary differential equations) 02.30.Mv (Approximations and expansions) 02.30.Sa (Functional analysis) 02.70.Wz (Symbolic computation (computer algebra))

套格图桑, 斯仁道尔吉, 李姝敏. New application to Riccati equation[J]. 中国物理B, 2010, 19(8): 80303-080303.

Taogetusang(套格图桑), Sirendaoerji(斯仁道尔吉), and Li Shu-Min(李姝敏). New application to Riccati equation[J]. Chin. Phys. B, 2010, 19(8): 80303-080303.

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New application to Riccati equation

New application to Riccati equation

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