An Exact Solution of the Hunter–Saxton–Calogero Equation by Contact Linearization Method

Authors

  • Svetlana Mukhina V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

DOI:

https://doi.org/10.25728/assa.2023.23.04.1504

Keywords:

Contact transformations, the Cartan form, nematic crystals, exact solution, nonlinear partial differential equation, differential forms

Abstract

In this paper we consider a class of generalized nonlinear hyperbolic partial differential equations of the Hunter–Saxton–Calogero type, which arise in the theory of control of liquid crystals and in the control of unsteady gas flows. We found such conditions that the original equation can be reduced to linear one by contact transformations. The general exact multivalued solutions of the Hunter–Saxton–Calogero equation are found. The obtained solutions are visualized.

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Published

2023-12-31

Issue

Vol. 23 No. 4 (2023): Advances in Systems Science and Applications

Section

Articles

How to Cite

An Exact Solution of the Hunter–Saxton–Calogero Equation by Contact Linearization Method. (2023). Advances in Systems Science and Applications, 23(4), 1-7. https://doi.org/10.25728/assa.2023.23.04.1504