E. V. Zemlyanaya

The generalized continuous analog of Newton’s method for the numerical study of some nonlinear quantum-field models

A numerical method for studying nonlinear problems arising in mathematical models of physics is systematically described in this review. The unified basis for the development of numerical schemes is a generalization of the continuous analog of Newton’s method, which represents a qualitatively new development of the Newtonian evolution process on the basis of the integration of concepts from perturbation theory and the theory of evolution in parameters. The results are presented of numerical studies of quantum-field models of the polaron, the solvated electron, the binucleon, and also QCD potential models for some commonly used potentials.

Calculations of 6He + p elastic-scattering cross-sections using folding approach and high-energy approximation for the optical potential

Abstract.Calculations of microscopic optical potentials (OPs) (their real and imaginary parts) are performed to analyze the 6He + p elastic-scattering data at a few tens of MeV/nucleon (MeV/N). The OPs and the cross-sections are calculated using three model densities of 6He . Effects of the regularization of the NN forces and their dependence on nuclear density are investigated. Also, the role of the spin-orbit terms and of the non-linearity in the calculations of the OPs, as well as effects of their renormalization are studied. The sensitivity of the cross-sections to the nuclear densities was tested and one of them that gives a better agreement with the data was chosen.

Oscillatory instabilities of gap solitons : a numerical study

We study stability of optical gap solitons, close relatives of spinor solitons of nonlinear classical field theory. The analysis of the associated linearized eigenvalue problem demonstrates the existence of a cascade of oscillatory and translational instabilities. The numerical technique involved is a combination of the Fourier transform and continuous analogue of Newtons method.

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions 16O on nuclei at an energy of E ∼ 100 MeV per nucleon.

Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary to periodic to quasiperiodic complexes.

Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.

Interactions of parametrically driven dark solitons. I. Néel-Néel and Bloch-Bloch interactions.

We study interactions between the dark solitons of the parametrically driven nonlinear Schrödinger equation, Eq. 1 . When the driving strength, h , is below sqrt[gamma(2)+1/9], two well-separated Néel walls may repel or attract. They repel if their initial separation 2z(0) is larger than the distance 2zu between the constituents in the unstable stationary complex of two walls. They attract and annihilate if 2z(0) is smaller than 2zu. Two Néel walls with h lying between sqrt[gamma(2)+1/9] and a threshold driving strength hsn attract for 2z(0)<2zu and evolve into a stable stationary bound state for 2z(0)>2zu. Finally, the Néel walls with h greater than hsn attract and annihilate-irrespective of their initial separation. Two Bloch walls of opposite chiralities attract, while Bloch walls of like chiralities repel-except near the critical driving strength, where the difference between the like-handed and oppositely handed walls becomes negligible. In this limit, similarly handed walls at large separations repel while those placed at shorter distances may start moving in the same direction or transmute into an oppositely handed pair and attract. The collision of two Bloch walls or two nondissipative Néel walls typically produces a quiescent or moving breather.

Travelling solitons in the externally driven nonlinear Schrödinger equation

We consider the undamped nonlinear Schr?dinger equation driven by a periodic external force. In the absence of damping, solitons do not have undulations on their tails; yet, we show that they can bind into stationary multisoliton complexes. Using two previously known stationary solitons and two newly found stationary complexes as starting points, we obtain classes of localized travelling waves by the numerical continuation in the parameter space. Two families of stable solitons are identified: one family is stable for sufficiently low velocities while solitons from the second family stabilize when travelling faster than a certain critical speed. The stable solitons of the former family can also form stably travelling bound states.

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