近似同伦对称方法与六阶Boussinesq方程的同伦级数解
Approximate homotopy symmetry method and homotopy series solutions to the six-order boussinesq equation
摘要：
提出一种求解非线性问题的近似同伦对称方法，并将其应用于六阶Boussinesq方程。总结了相似约化解和不同阶相似约化方程的一般公式，导出了相关的同伦级数解。同伦级数解的收敛区域可以通过辅助参数来调节。近似对称方法的级数解和相似约化方程可以由近似同伦对称方法得到。
英文摘要：
An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the six-order boussinesq equation. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. The convergence region of homotopy series solutions can be adjusted by the auxiliary parameter. Series solutions and similarity reduction equations from approximate symmetry method can be retrieved from approximate homotopy symmetry method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
