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conservation form of Helbing's fluid dynamic traffic flow model

Applied Mathematics and Mechanics(English Edition) 2011年第9期32卷 1109-1118页

作者：李书峰张鹏 S.C.WONG Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Department of Civil Engineering The University of Hong Kong

A standard conservation form is derived in this *** hyperbolicity of Helbing＇s fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this *** the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting system *** evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is *** simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients,and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.

关键词： conservation form hyperbolicity local discontinuous Galerkin method stop-and-go wave

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Higher-dimensional integrable deformations of the modified KdV equation

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Communications in Theoretical Physics 2023年第7期75卷 15-21页

作者： Xiazhi Hao S Y Lou College of Science Zhejiang University of TechnologyHangzhouChina School of Physical Science and Technology Ningbo UniversityNingbo315211China

The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of *** well-known modified Kd V equation is a prototypical example of an integrable evolution equation in one spatial *** there exist integrable analogs of the modified Kd V equation in higher spatial dimensions?In what follows,we present a positive answer to this *** particular,rewriting the(1+1)-dimensional integrable modified Kd V equation in conservation forms and adding deformation mappings during the process allows one to construct higher-dimensional integrable ***,we illustrate this idea with examples from the modified Kd V hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.

关键词： higher-dimensional integrable equation conservation form deformation mapping Lax integrability symmetry integrability

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