A new nonlinear integrable fifth-order equation with temporal and spatial dispersion is investigated, which can be used to describe shallow water waves moving in both directions. By performing the singularity manifold analysis, we demonstrate that this generalized model is integrable in the sense of Painlevé for one set of parametric choices. The simplified Hirota method is employed to construct the one-, two-, three-soliton solutions with non-typical phase shifts. Subsequently, an extended projective Riccati expansion method is presented and abundant travelling wave solutions are constructed uniformly. Furthermore, several new interaction solutions between periodic waves and kinky waves are also derived via a direct method. The rich interactions including overtaking collision, head-on collision and periodic-soliton collision are analyzed by some graphs.

研究了一个具有时间和空间色散的新的非线性可积五阶方程，该方程可用于描述在两个方向上移动的浅水波。通过执行奇异性流形分析，我们证明对于一组参数选择，该广义模型在Painlevé的意义上是可集成的。简化的Hirota方法用于构造具有非典型相移的一，二，三孤子解。随后，提出了一种扩展的射影Riccati展开方法，并均匀构造了丰富的行波解。此外，还通过直接方法得出了周期波和扭波之间的几种新的相互作用解。丰富的互动，包括超越碰撞，