Related papers: Collective Coordinate Methods and Their Applicabil…
We obtain exact traveling-wave solutions of the coupled nonlinear partial differential equations that describe the dynamics of two classical scalar fields in 1+1 dimensions. The solutions are kinks interpolating between neighboring vacua.…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
In the Bogomol'nyi limit of the Calogero-Sutherland collective-field model we find static-soliton solutions. The solutions of the equations of motion are moving solitons, having no static limit for $\l>1$. They describe holes and lumps,…
The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon…
A strong magnetic field can make it advantageous to work in a coordinate system aligned with dipolar field lines. This monograph collect the formulas for some of the most frequently used expressions and operations in dipole coordinates.
We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the…
We use the quantum group approach for the investigation of correlation functions of integrable vertex models and spin chains. For the inhomogeneous reduced density matrix in case of an arbitrary simple Lie algebra we find functional…
We propose new measures of localization and cooperativity for the analysis of atomic rearrangements. We show that for both clusters and bulk material cooperative rearrangements usually have significantly lower barriers than uncooperative…
In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe inhomogeneous accelerating sections. It was shown that the single mode…
The description of FELWI in the collective approach, is given The dispersion equations are obtained and discussed for both Raman and Thompson regimes.
We study soliton interaction in the Modified Kadomtsev-Petviashvili-(II) equation (MKP-(II)) using the totally non-negative Grassmannian. One constructs the multi-kink soliton of MKP equation using the $\tau$-function and the Binet-Cauchy…
A model to study the dynamics of colloidal particles in nonuniform electric fields is proposed. For an isolated sphere, the conditions and threshold for sustained (Quincke) rotation in a linear direct current (dc) field are determined.…
We study various properties of topological solitons (kinks) of a field-theoretic model with a polynomial potential of the twelfth degree. This model is remarkable in that it has several topological sectors, in which kinks have different…
Contact detection for continuum and soft robots has been limited in past works to statics or kinematics-based methods with assumed circular bending curvature or known bending profiles. In this paper, we adapt the generalized momentum…
Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models…
Quantum cooperativity is evident in light-matter platforms where quantum emitter ensembles are interfaced with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum. Cooperative effects can find…
Octupole deformation and collective excitations are studied within the interacting boson model. By using the results of the self-consistent mean-field calculations with a universal energy density functional, the Hamiltonian of the…
Standard weak coupling methods are used to study collective modes in the superconducting state of a double-layer system with intralayer and interlayer interaction, as well as a Josephson-type coupling and single particle hopping between the…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…