Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform

Leonid Nizhnik

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arXiv · 2412.16801

Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform

Leonid Nizhnik

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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.

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Leonid Nizhnik. 2024-12-21. Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform. https://arxiv.org/abs/2412.16801

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