# Semiclassical WKB Problem for the Non-Self-Adjoint Dirac Operator with a Multi-Humped Decaying Potential

@inproceedings{Hatzizisis2021SemiclassicalWP, title={Semiclassical WKB Problem for the Non-Self-Adjoint Dirac Operator with a Multi-Humped Decaying Potential}, author={Nicholas Hatzizisis and Spyridon Kamvissis}, year={2021} }

In this paper we continue the study (initiated in [8]) of the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a real, positive, fairly smooth but not necessarily analytic potential decaying at infinity; in this paper we allow this potential to have several local maxima and minima. We provide the rigorous semiclassical analysis of the Bohr-Sommerfeld condition for the location of the eigenvalues, the norming constants, and the reflection coefficient.

#### Figures from this paper

#### References

SHOWING 1-10 OF 23 REFERENCES

Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential

- Physics, Mathematics
- 2019

In this paper we examine the semiclassical behaviour of the scattering data of a non-self-adjoint Dirac operator with analytic potential decaying at infinity. In particular, employing the exact WKB… Expand

Semiclassical WKB problem for the non-self-adjoint Dirac operator with a decaying potential

- Physics, Mathematics
- 2020

In this paper we examine the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a fairly smooth -but not necessarily analyticpotential decaying at infinity. In… Expand

The semiclassical limit of eigenfunctions of the Schr

- Mathematics
- 2010

Consider the semiclassical limit, as the Planck constant $\hbar\ri 0$, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of… Expand

Some remarks on a WKB method for the nonselfadjoint Zakharov–Shabat eigenvalue problem with analytic potentials and fast phase

- Mathematics
- 2001

Abstract A formal method for approximating eigenvalues of the nonselfadjoint Zakharov–Shabat eigenvalue problem in the semiclassical scaling is described. Analyticity of the potential is assumed and… Expand

Existence and Regularity for an Energy Maximization Problem in Two Dimensions

- Mathematics, Physics
- 2005

We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a particular external… Expand

Passage through a potential barrier and multiple wells

- Mathematics, Physics
- 2016

Consider the semiclassical limit, as the Planck constant $\hbar\ri 0$, of bound states of a one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each… Expand

Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation

- Mathematics, Physics
- 2000

This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic… Expand

Universality for the focusing nonlinear Schroedinger equation at the gradient catastrophe point: Rational breathers and poles of the tritronquee solution to Painleve I

- Mathematics, Physics
- 2010

The semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials is studied in a full scaling neighborhood D of the point of… Expand

Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media

- Physics
- 1970

It is demonstrated that the equation iol/J/ot + l/Jxx + K 1¢12 1/1 = 0, which describes plane self-focusing and one-dimensional self-modulation can be solved exactly by reducing it to the inverse… Expand

On the Eigenvalues of Zakharov-Shabat Systems

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2003

Best possible lower bounds on the number of eigenvalues for a real potential of one sign are obtained, exact for the class of single lobe potentials, that is, positive potentials with a single local maximum that is also global. Expand