带流体动力学阻尼的IBq方程的精确解

doi:10.12068/j.issn.1005-3026.2017.10.030

东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (10): 1516-1520.DOI: 10.12068/j.issn.1005-3026.2017.10.030

• 数学 • 上一篇

带流体动力学阻尼的IBq方程的精确解

宋叔尼¹，范凯²

(1. 东北大学理学院，辽宁沈阳110819; 2. 太原科技大学应用科学学院，山西太原030024)

收稿日期:2016-05-11 修回日期:2016-05-11 出版日期:2017-10-15 发布日期:2017-10-13
通讯作者: 宋叔尼
作者简介:宋叔尼(1962-)，男，湖南澧县人，东北大学教授.
基金资助:
辽宁省自然科学基金资助项目(201602259).

Exact Solutions for IBq Equation with Fluid Dynamic Damping

SONG Shu-ni¹， FAN Kai²

1. School of Sciences， Northeastern University， Shenyang 110819， China; 2. School of Applied Science， Taiyuan University of Science and Technology， Taiyuan 030024， China.

Received:2016-05-11 Revised:2016-05-11 Online:2017-10-15 Published:2017-10-13
Contact: FAN Kai
About author:-
Supported by:
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摘要/Abstract

摘要： 对带流体动力学阻尼的IBq方程进行了研究，发现虽然对Bq方程精确解的研究很多，但对IBq方程解的研究结果却很少.介绍了求解非线性演化方程的Tanh法与扩展Tanh函数法，使用符号计算软件Maple和Tanh函数法获得带流体动力学阻尼的IBq方程的大量双曲函数精确解，主要为扭结和反扭结孤立子解.对精确解中未知参数进行赋值，图解表示了部分精确解，这对于数值解的准确性和稳定性的核对是有用的.获得的结果证实该方法用于分析求解数学物理中各种非线性偏微分方程是有效的.

关键词: Tanh函数法, 扩展Tanh函数法, 双曲函数精确解, IBq方程, 流体动力学阻尼

Abstract: The IBq equation with fluid dynamic damping was studied. Many studies of exact solutions for Bq equation were found， but the study results of the IBq equations were very few. The standard Tanh method and the extended Tanh method were introduced to solve nonlinear evolution equation， and the standard Tanh method and symbolic computation system Maple were used to obtain a large number of exact hyperbolic function solutions of IBq equation with fluid dynamic damping， mainly for the kink and the antikink soliton solutions. Assignment of exact solutions was done for the unknown parameters， and figures showed some exact solutions， which were useful for verifying the accuracy and stability of numerical solution. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics.

Key words: Tanh method, extended Tanh method, exact hyperbolic function solutions, IBq equation, fluid dynamic damping

中图分类号:

O175.29

宋叔尼，范凯. 带流体动力学阻尼的IBq方程的精确解[J]. 东北大学学报:自然科学版, 2017, 38(10): 1516-1520.

SONG Shu-ni， FAN Kai. Exact Solutions for IBq Equation with Fluid Dynamic Damping[J]. Journal of Northeastern University Natural Science, 2017, 38(10): 1516-1520.

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带流体动力学阻尼的IBq方程的精确解

Exact Solutions for IBq Equation with Fluid Dynamic Damping

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