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A new hyperbolic equation possessing a zero-curvature representation

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Using a direct procedure of calculation of zero-curvature representations (ZCR), we find a previously unknown hyperbolic equation which possesses an \(\mathfrak{s}\mathfrak{l}_2 \)-valued ZCR. This ZCR admits no parameters and is not reducible to a proper subalgebra of \(\mathfrak{s}\mathfrak{l}_2 \).

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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.

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Pobořil, M. A new hyperbolic equation possessing a zero-curvature representation. J Math Sci 136, 4484–4485 (2006).

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  • Normal Form
  • Hyperbolic Equation
  • Nonlinear Hyperbolic Equation
  • Direct Procedure
  • Linear Covering