A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields
S. V. Manakov, P. M. Santini
TL;DR
This paper introduces a new hierarchy of integrable partial differential equations in 2+1 dimensions linked to 2D vector fields, and solves their Cauchy problems using an advanced inverse scattering method.
Contribution
It presents a novel hierarchy of integrable PDEs in higher dimensions and applies a recent inverse scattering transform to solve their initial value problems.
Findings
Established a hierarchy of integrable PDEs in 2+1 dimensions.
Successfully solved the associated Cauchy problems.
Extended inverse scattering techniques to multidimensional vector fields.
Abstract
We introduce a hierarchy of integrable PDEs in 2+1 dimensions arising from the commutation of 2-dimensional vector fields. We also solve the associated Cauchy problems, using the recently developed Inverse Scattering Transform for 1-parameter families of multidimensional vector fields.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Algebraic structures and combinatorial models