Related papers: Twisted kinks, Dirac transparent systems and Darbo…
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…
The numerical discretization of the Zakharov-Shabat Scattering problem using integrators based on the implicit Euler method, trapezoidal rule and the split-Magnus method yield discrete systems that qualify as Ablowitz-Ladik systems. These…
For the nonlinear Klein-Gordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are therefore free of the {\it static}…
Following on from previous work we derive the non-linear differential equations of more general correlators of U(1) twist fields in two-dimensional massive Dirac theory. Using the conserved charges of the double copy model equations…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system which can be interpreted as a one-parameter deformation of the…
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related…
Using the Darboux method and its relation with supersymmetric quantum mechanics we construct all SUSY partners of the harmonic oscillator. With the help of the SUSY transformation we introduce ladder operators for these partner Hamiltonians…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
In this letter, we show how to build bridges between field-theoretic models that have kink solutions with different asymptotic behavior. We study transformational properties of kinks in models with a real scalar field in two-dimensional…
The zero-range potentials of the radial Schrodinger equation are investigated from a point of Darboux transformations scheme. The dressing procedure is realized as a sequence of Darboux transformations in a way similar to that used to…
We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic nonlinearity. We show that, with the nonlinearity parameters specifically tuned, a high degree of localization of both spinor components is enabled on a…
We show that 2+1 dimensional Dirac oscillators in an external magnetic field is mapped onto the same with reduced angular frequency in absence of magnetic field. This can be used to study the atomic transitions in a radiation field.…
Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems, non-perturbative solutions of various large-N field theories, and closely related solitonic solutions to the Bogoliubov-de…
We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form…
Symmetries and solutions of the Painleve IV equation are presented in an alternative framework which provides the bridge between the Hamiltonian formalism and the symmetric Painleve IV equation. This approach originates from a method…
We prove that second-order hyperbolic Monge-Ampere equations for one function of two variables are connected to the wave equation by a Backlund transformation if and only if they are integrable by the method of Darboux at second order. One…