Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform
Exactly Solvable and Integrable Systems
2024-12-24 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
The Hamiltonian form of the (2+1) nonlinear integrable Schr\"odinger equation and the system of two (2+1) nonlinear analogue of the mKdV equation is proved. A well--posed Cauchy problem is formulated and the solvability of such a problem for the (2+1) nonlinear analogue of the mKdV equation is proved.
Keywords
Cite
@article{arxiv.2412.16801,
title = {Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform},
author = {Leonid Nizhnik},
journal= {arXiv preprint arXiv:2412.16801},
year = {2024}
}