Abstract
Bores propagating in shallow water transform into undular bores and, finally, into trains of solitons. The observed number and height of these undulations and later discrete solitons are strongly dependent on the propagation length of the bore. Empirical results show that the final height of the leading soliton in the far-field is twice the initial mean bore height. The complete disintegration of the initial bore into a train of solitons requires very long propagation, but unfortunately, these required distances are usually not available in experimental tests of nature. Therefore, the analysis of the bore decomposition for experimental data into solitons is complicated and requires different approaches. Previous studies have shown that by applying the nonlinear Fourier transform based on the Ko- rteweg–de Vries equation (KdV-NFT) to bores and long-period waves propagating in constant depth, the number and height of all solitons can be reliably predicted already based on the initial bore-shaped free surface. Against this background, this study presents the systematic analysis of the leading-soliton amplitudes for non-breaking and breaking bores with different strengths in different water depths to validate the KdV-NFT results for non-breaking bores to show the limitations of wave breaking on the spectral results. The analytical results are compared with data from experimental tests, numerical simulations and other approaches from the literature.
Highlights
A nonlinear problem is critical in all areas of mathematics and physics
To replicate the nonlinear scattering wavefront issues mentioned by the KdVB equations in (Li & Visbal, 2006), more excellent compact variational strategies were combined with a higher top filter and the traditional fourth order Runge-Kutta arrangement
This paper presented a technique to calculate fifth order KDV equations, fifth order nonhomogeneous KDV equations, and Kawahara's formula combining Laplace transform with homogeneous perturbation
Summary
A nonlinear problem is critical in all areas of mathematics and physics. The complexity of physical processes hides the majority of the exciting consequences. A greater portable variation mechanism for various derivatives based on implicit interpolations was developed in 1992 (Lele, 1992) Such ambiguous strategies were precise inhomogeneous areas and had frequency pixel density properties when using the worldwide matrix. The merits of our current method for the KdVB equation are demonstrated in this paper, and contrast of numerical methods with the optimal solution is performed to demonstrate the method's capability for nonlinear dispersive equations. This equation is commonly referred to as the Rosenau-KdV equation. The ansatz procedure (Lele 1992) used This paper uses linear functions to discuss real-world applications, including essential characteristics and how to graph them from various forms
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