Rational KdV Potentials and Differential Galois Theory
Copyright policy )Rational KdV Potentials and Differential Galois Theory
In this work, using differential Galois theory, we study the spectral problem of the one-dimensional Schr��dinger equation for rational time dependent KdV potentials. In particular, we compute the fundamental matrices of the linear systems associated to the Schr��dinger equation. Furthermore we prove the invariance of the Galois groups with respect to time, to generic values of the spectral parameter and to Darboux transformations.
Schrödinger operator, Soliton equations, Matemáticas, 12H05, 35Q51, 37K10, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), Differential Galois theory, Differential algebra, differential Galois theory, Darboux transformations, KdV hierarchy, rational solitons, Spectral curves, Rational solitons, spectral curves, Mathematical Physics
Schrödinger operator, Soliton equations, Matemáticas, 12H05, 35Q51, 37K10, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), Differential Galois theory, Differential algebra, differential Galois theory, Darboux transformations, KdV hierarchy, rational solitons, Spectral curves, Rational solitons, spectral curves, Mathematical Physics
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