【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.更多还原

【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.更多还原