In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for this equation. We readily obtain Bcklund transformation associated with truncated Painlev expansion. We also examine the related conservation laws of this equation via using the multiplier method. Moreover, we investigate the reciprocal Bcklund transformations of the derived conservation laws for the first time.

在这项工作中，我们研究了广义双色散Boussinesq方程，该方程在流体力学，科学领域和海洋工程中发挥着重要作用。通过使用扰动分析，该方程将简化为Korteweg-de Vries方程。我们推导了该方程的相应向量，对称约简和显式解。我们很容易获得与截断的Painlev展开有关的Bcklund变换。我们还使用乘数法研究了该方程的相关守恒律。此外，我们首次研究了导出的守恒律的倒数Bcklund变换。