The ABC-equation revisited: missed integrable cases. Part I: classification and (quasi) integrable structures
I. S. Krasil'shchik
Abstract
We consider the ABC-equation Auxuyt + Buyuxt + Cutuxy = 0, A, B, C∈R, which was proved to be integrable in the case A + B + C = 0 (the Veronese web equation). Our study reveals ten more cases that admit integrable structures that, to the best of our knowledge, where not known before. The techniques is based essentially on the theory of the tangent and cotangent coverings.
Create a lesson
Related papers
Symmetries, Lax pair, and nilpotent Darboux transformation for the KdV-ghost system
A. Restuccia, J. Rosales-Gómez, A. Sotomayor
Long-time asymptotics for the focusing coupled Kundu-Eckhaus equation
Tianwei Qiu, Zhen Wang
Higher-order semi-rational solutions of the (2+1)-dimensional nonlocal multi-component Yajima--Oikawa system
Wenqiang Lu, Kelei Tian, Ying Xu et al.
On equivalence between solution structures of the anti-self-dual Yang--Mills equations
Shangshuai Li
Nonlinear Spectral Computing
Ludovica Falsi, Francesco Coppini, Claudio Conti
The Riemann theta function near soliton limit
Yuji Kodama