Journal
STUDIES IN APPLIED MATHEMATICS
Volume 148, Issue 2, Pages 758-772Publisher
WILEY
DOI: 10.1111/sapm.12457
Keywords
conservation laws; equations describing pseudo-spherical surfaces; geometric integrability; local isometric immersions
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Funding
- Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior - Brasil (CAPES) [FinanceCode 001]
- FAPESP [2020/02055-0]
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This study demonstrates that an equation discovered by V. Novikov describes pseudo-spherical surfaces and is geometrically integrable, resulting in an infinite hierarchy of conservation laws. The problem of local isometric immersions is also examined in the context of this equation.
We show that an equation discovered in V. Novikov [Generalizations of the Camassa-Holm equation, J Phys A: Math Theor. 2009; 42: paper 342002] describes pseudo-spherical surfaces and is geometrically integrable. From the geometric structure of the equation we obtain an infinite hierarchy of conservation laws. The problem of local isometric immersions is also considered.
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