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Bidirectional solitons and interaction solutions for a new integrable fifth-order nonlinear equation with temporal and spatial dispersion

机译：具有时间和空间分散的新可接受的第五阶非线性方程的双向孤子和交互解决方案

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摘要

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 Painleve 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.
机译：研究了具有时间和空间分散的新的非线性可接定的第五阶方程，其可用于描述在两个方向上移动的浅水波。 通过执行奇点歧管分析，我们证明该广义模型在一组参数选择的痛苦感中是可集成的。 使用简化的HiROTA方法来构建具有非典型相移的单个，双孤子溶液。 随后，提出了扩展的投影Riccati扩展方法，并且均匀地构造了丰富的行波解决方案。 此外，周期性波和扭曲波之间的几个新的相互作用解决方案也通过直接方法导出。 通过一些图表分析了具有超越碰撞，头部碰撞和周期性孤子碰撞的丰富的相互作用。

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