Volume 7, Issue 1, February 2000, Pages 1 - 13
Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation
Song-Ju Yu, Kouichi Toda
Received 4 May 1999, Revised 13 June 1999, Accepted 14 July 1999, Available Online 1 February 2000.
- 10.2991/jnmp.2000.7.1.1How to use a DOI?
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 Painlevé property. Some exact solutions are also constructed.
- © 2006, the Authors. Published by Atlantis Press.
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Cite this article
TY - JOUR AU - Song-Ju Yu AU - Kouichi Toda PY - 2000 DA - 2000/02/01 TI - Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation JO - Journal of Nonlinear Mathematical Physics SP - 1 EP - 13 VL - 7 IS - 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2000.7.1.1 DO - 10.2991/jnmp.2000.7.1.1 ID - Yu2000 ER -