Analysis of wave propagation and conservation laws for a shallow water model with two velocities via Lie symmetry

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-24 DOI:10.1016/j.cnsns.2025.108637

Aniruddha Kumar Sharma, Sumanta Shagolshem, Rajan Arora

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引用次数: 0

Abstract

This research investigates a one-dimensional system of quasi-linear hyperbolic partial differential equations, obtained by vertically averaging the Euler equations between artificial interfaces. This system represents a shallow water model with two velocities and is explored using Lie symmetry analysis to derive several closed-form solutions. Through symmetry analysis, a Lie group of transformations and its corresponding generators are identified via parameter analysis. From these, an optimal one-dimensional system of subalgebras is constructed and classified based on symmetry generators and invariant functions. The model is further simplified by reducing it to ordinary differential equations (ODEs) using similarity variables for each subalgebra, yielding invariant solutions. Additionally, various conservation laws are formulated utilizing the nonlinear self-adjointness property of the governing system. The study concludes by analyzing the behavior of characteristic shocks, C1-waves, and their interactions, offering a detailed understanding of their dynamics.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.