Construction of reflectionless potentials with infinite discrete spectrum

DOI10.1007/BF01016760zbMath0857.34073MaRDI QIDQ1920715

A. B. Shabat, Antonio Degasperis

Publication date: 17 March 1997

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

one-dimensional Schrödinger operatorDarboux transformationinfinitely many eigenvalues

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Dispersion theory, dispersion relations arising in quantum theory (81U30)

Related Items (12)

A New Class of Soliton Solutions for the (Modified) Kadomtsev-Petviashvili Equation ⋮ High order stable Runge-Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ⋮ The Riemann problem and matrix-valued potentials with a convergent Baker-Akhiezer function ⋮ Discrete symmetries and solitons ⋮ Local realizations of \(q\)-oscillators in quantum mechanics ⋮ Small divisors problem in dynamical systems and analytic solutions of the Shabat equation ⋮ A nonlinear eigenvalue problem ⋮ Reflectionless sine-Gordon potentials with an infinite spectrum ⋮ The dressing chain of discrete symmetries and proliferation of nonlinear equations ⋮ Toda soliton limits on general backgrounds ⋮ Regular solutions of the Shabat equation ⋮ Soliton Theory and Hankel Operators

Cites Work

• The infinite-dimensional dressing dynamical system
• Painleve analysis and singularity confinement: the ultimate conjecture
• Wavelets and Dilation Equations: A Brief Introduction
• The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$
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