The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field. By choosing the function f in Hirota bilinear form, as the general quadratic function, trigonometric function and exponential function along with appropriate set of parameters, we find the lump, lump-one stripe, multiwave and breather solutions successfully. We also interpreted some three-dimensional and contour profiles to anticipate the wave dynamics. These newly obtained solutions have some arbitrary constants and so can be applicable to explain diversity in qualitative features of wave phenomena.

中文翻译：

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亨特-萨克斯顿方程的总，总一条纹，多波和通气解

本文的目的是借助Hirota双线性技术来解决Hunter-Saxton方程的块，块一，多波和通气解。该模型涉及大量的向列液晶指向矢领域。通过选择Hirota双线性形式的函数f作为一般的二次函数，三角函数和指数函数以及适当的参数集，我们成功地找到了块，块一条纹，多波和通气解。我们还解释了一些三维轮廓轮廓以预测波浪动力学。这些新获得的解具有一些任意常数，因此可用于解释波动现象的定性特征中的多样性。