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This research aims to analyze the Bateman-Burgers equation using symmetry methods, focusing on shock fronts and wave solutions.

The study of shock fronts and diffusive soliton waves to energy dissipation along with invariance classification

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This research aims to analyze the Bateman-Burgers equation using symmetry methods, focusing on shock fronts and wave solutions.
Conducted a Lie symmetry analysis of the Bateman-Burgers equation
Utilized similarity transformations to reduce partial differential equations
Applied the generalized logistic method and Riccati-Bernoulli technique for solitary wave solutions.
Developed a five-dimensional symmetry algebra encompassing translation, scaling, and dilation symmetries
Derived novel invariant solitary wave solutions that are unique and possess invariance properties
Classified solution families that exhibit distinct nonlinear dynamics and cannot be transformed through symmetry operations.

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Analytical investigation explores shock formation and wave solutions in fluid dynamics, indicating rich nonlinear behavior.

Faridi et al. (2026) studied this question.

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