可积（3+1）维五阶非线性海浪模型在空间变化背景下的块和孤子
Lump and Soliton on Certain Spatially-varying Backgrounds for an Integrable (3+1) Dimensional Fifth-order Nonlinear Oceanic Wave Model
摘要：
具有可控色散、非线性和背景的非线性波动力学是近年来的一个令人兴奋的研究方向。在这项工作中，我们专注于研究一个可积的（3+1）维非线性模型描述的{水波}的高阶时间色散的演变，通过表征不同的空间变化的背景下的块波和孤子波的动力学。我们构造显式块波和扭结孤子解所考虑的模型，通过其三线性和双线性方程与适当形式的多项式和指数型初始种子解，分别。此外，通过双线性贝克隆变换得到了双曲波和周期波。我们通过分类分析和清晰的图形演示来探索它们在空间背景下的传播和变换动力学，以充分理解由此产生的解决方案。我们的分析表明，在恒定的背景下，集总解导致同时存在的局部尖峰和下降（耦合亮暗型波）结构，而孤子解沿不同的时空域具有可控的属性表现出扭结和反扭结波图案。当适当地引入任意空间背景时，我们可以看到孤子表现为周期性的相互作用的动力学结构。另一方面，由于周期性和局部化的空间背景，块波导致共存、相互作用波和呼吸子的形成。结果将是一个重要的除了上下文的非线性波可控背景的高维模型。此外，本研究可以扩展到调查其他几个非线性系统，以了解其动态的变量背景的物理见解。
英文摘要：
The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model describing the evolution of {water waves} with higher-order temporal dispersion by characterizing the dynamics of lump and soliton waves on different spatially-varying backgrounds. We construct explicit lump wave and kink-soliton solutions for the considered model through its trilinear and bilinear equations with appropriate forms of the polynomial and exponential-type initial seed solutions, respectively. Additionally, we obtain hyperbolic and periodic waves through bilinear Bäcklund transformation. We explore their propagation and transformation dynamics with spatial backgrounds through a categorical analysis and clear graphical demonstrations to fully understand the resulting solutions. Our analysis shows that the lump solution results into a simultaneous existence of well-localized spike and declining (coupled bright-dark type wave) structures on a constant background, while the soliton solution exhibits kink and anti-kink wave patterns along different spatio-temporal domains with controllable properties. When the arbitrary spatial background is incorporated appropriately, we can witness the manifestation of soliton into periodic and interacting dynamical structures. On the other hand, the lump wave results into the coexistence, interacting wave and breather formation due to periodic and localized type spatial backgrounds. The results will be an important addition to the context of nonlinear waves with controllable backgrounds in higher-dimensional models. Further, the present study can be extended to investigate several other nonlinear systems to understand the physical insights of the variable background in their dynamics.
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