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<p>The principal focus of this work is to explore numerical solutions of the classical Whitham-Broer-Kaup equations using the local discontinuous Galerkin method. The numerical methodology employs an explicit strong-stability-preserving higher-order Runge-Kutta method to estimate the temporal derivatives and the local discontinuous Galerkin method to estimate the spatial derivatives, generating a large coupled ordinary differential equations system. The analytical improved <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6024_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\( (G'/G) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mi>G</mi> <mo>′</mo> </msup> <mo stretchy="false">/</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-expansion technique is also employed in this article to obtain new exact travelling wave solutions of the governing coupled Whitham-Broer-Kaup equations. Finally, some numerical experiments are performed, and all the simulation results are displayed in several tables and various two-dimensional and three-dimensional plots, which validate the satisfactory accuracy and efficacy of the implemented method.</p>

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Analytical and Numerical Solutions of the Whitham-Broer-Kaup System for Long Waves in Small-amplitude Shallow Water

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Abhilash Chand,
  • Jugal Mohapatra

摘要

The principal focus of this work is to explore numerical solutions of the classical Whitham-Broer-Kaup equations using the local discontinuous Galerkin method. The numerical methodology employs an explicit strong-stability-preserving higher-order Runge-Kutta method to estimate the temporal derivatives and the local discontinuous Galerkin method to estimate the spatial derivatives, generating a large coupled ordinary differential equations system. The analytical improved \( (G'/G) \) ( G ′ / G ) -expansion technique is also employed in this article to obtain new exact travelling wave solutions of the governing coupled Whitham-Broer-Kaup equations. Finally, some numerical experiments are performed, and all the simulation results are displayed in several tables and various two-dimensional and three-dimensional plots, which validate the satisfactory accuracy and efficacy of the implemented method.