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中文摘要：
基于双曲函数法的思想,通过选择新的展开函数,得到了modified Korteweg-de Vries（mKdV）方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为mKdV方程的扭结状或钟状孤波解.文中对双扭结型孤子解的稳定性进行了数值研究,结果表明：在长波和短波简谐波扰动、钟型孤立波扰动与随机扰动下,该孤子均稳定.
英文摘要：
Based on the idea of the hyperbola function expansion method,some analytical solutions of the modified Korteweg-de Vries （mKdV） equation are obtained by introducing new expansion functions.One of the single soliton solutions has a kink-antikink structure and it reduces to a kink-like solution and bell-like solution under different limitations.The stability of the single soliton solution with double kinks is investigated numerically.The results indicate that the soliton is stable under different disturbances.
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