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Lax pairs, Painlev\'e properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation

Song-Ju Yu·Kouichi Toda
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Abstract

We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV equation are integrable in the sense that they possess the Painlev\'e property. Some exact solutions are also constructed.

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Song-Ju Yu, Kouichi Toda. 2000-01-01. Lax pairs, Painlev\'e properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation. https://doi.org/10.2991/jnmp.2000.7.1.1

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