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2019•Communications in Theoretical PhysicsRequires access

An Integrable Matrix Camassa-Holm Equation*

Li-Feng Chan, Baoqiang Xia, Ruguang Zhou

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Abstract

Abstract We present an integrable sl (2)-matrix Camassa-Holm (CH) equation. The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws. This equation includes two undetermined functions, which satisfy a system of constraint conditions and may be reduced to a lot of known multi-component peakon equations. We find a method to construct constraint condition and thus obtain many novel matrix CH equations. For the trivial reduction matrix CH equation we construct its N-peakon solutions.

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Abstract We present an integrable sl (2)-matrix Camassa-Holm (CH) equation. The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws. This equation includes two undetermined functions, which satisfy a system of constraint conditions and may be reduced to a lot of known multi-component peakon equations. We find a method to construct constraint condition and thus obtain many novel matrix CH equations. For the trivial reduction matrix CH equation we construct its N-peakon solutions.

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Available abstract

Abstract We present an integrable sl (2)-matrix Camassa-Holm (CH) equation. The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws. This equation includes two undetermined functions, which satisfy a system of constraint conditions and may be reduced to a lot of known multi-component peakon equations. We find a method to construct constraint condition and thus obtain many novel matrix CH equations. For the trivial reduction matrix CH equation we construct its N-peakon solutions.

Key concepts: Peakon, Camassa–Holm equation, Integrable system, Matrix (chemical analysis), Construct (python library), Constraint (computer-aided design), Mathematics, Curvature

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