The nonlinear Schrödinger equation (NLSE) with a non-Hermitian term is the model for various phenomena in open quantum systems. We deal Cauchy problem nonlocal generalization of multidimensional NLSE term. Using ideas Maslov method, we propose method constructing asymptotic solutions to this within framework semiclassically concentrated states. semiclassical evolution operator and symmetry operators leading asymptotics are derived. Our approach based on auxiliary dynamical system that...

The generalized Haus equation is considered, which accounts for the non-stationarity of active medium pumping conditions. We propose an approach to construction asymptotic solutions such based on method semiclassically concentrated states. For this purpose, model presented in a nonlocal form, and various options relation between parameters small parameter semiclassical approximation are considered. equations terms expansion envelope laser radiation mode cavity obtained explicit way. proposed...

In this paper, we propose an approach for constructing quasiparticle-like asymptotic solutions within the weak diffusion approximation generalized population Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation, which incorporates nonlocal quadratic competitive losses and a fractal time derivative of non-integer order (α, where 0<α≤1). This is based on semiclassical principles Maslov method. The introduced in framework Fα calculus. Fisher–KPP equation decomposed into system...

Abstract We construct quasiparticles-like solutions to the one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) with a nonlocal nonlinearity using method of semiclassically concentrated states in weak diffusion approximation. Such are use for predicting dynamics population patterns analytical or semi-analytical approach. The interaction quasiparticles stems from competitive losses FKPP model. developed formalism our approach relying on ideas Maslov method. construction asymptotic...

Discrete kinetic equations describing binary processes of agglomeration and fragmentation are considered using formal equivalence between the geodesic some affinely connected space A associated with equation called affine connection. The geometric properties treated locally in coordinate chart (x;U). peculiarity is that coordinates (x) selected local chart, Christoffel symbols defining connection constant. Examples Smoluchowski for without exchange-driven growth small dimensions terms...

We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The with an invariant metric is shown to be equivalent system of equations on Lie group transformations space. This allows us effectively apply linear partial differential groups. differs from well-known separation variables and some extent can often supplement it. general structure developed illustrated example space which does not admit equation. However, basis exact solutions constructed...

The general construction of semiclassically concentrated solutions to the Hartree type equation, based on complex WKB‐Maslov method, is presented. formal Cauchy problem for this asymptotic in small parameter ℏ ( → 0), are constructed with a power accuracy O N /2 ), where any natural number. In constructing solutions, set Hamilton‐Ehrenfest equations (equations centered moments) essentially used. nonlinear superposition principle has been formulated class equations. results obtained...

The ability to diagnose oral lichen planus (OLP) based on saliva analysis using THz time-domain spectroscopy and chemometrics is discussed. study involved 30 patients (2 male 28 female) with OLP. This group consisted of two subgroups the erosive form OLP (n = 15) reticular papular forms 15). control six healthy volunteers (one five females) without inflammation in mucous membrane cavity periodontitis. Principal component was used reveal informative features experimental data. one-versus-one...

The results of numerical simulation application principal component analysis to absorption spectra breath air patients with pulmonary diseases are presented. Various methods experimental data preprocessing analyzed.

We explore in detail the creation of stable localized structures form energy distributions that arise from general initial conditions Peyrard-Bishop (PB) model. By means a method based on inverse scattering transform we study solutions PB model equations obtained planar waves whose amplitudes are described by nonlinear Schr\"odinger equation (NLS). For different pure $N$-soliton shape, have analytical results predict and control number, amplitude, velocity NLS solitary waves. To verify...

Integration of the Dirac equation with an external electromagnetic field is explored in framework method separation variables and noncommutative integration. We have found a new type solutions that are not obtained by for several fields. considered example crossed electric magnetic fields special which admits nonlocal symmetry operator.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for 1D nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation under supposition of weak diffusion. In terms formalism developed, original nonlinear reduced to an associated linear partial differential and some algebraic equations coefficients with a given accuracy asymptotic parameter. The solutions are constructed from both equations. problem found use symmetry operators. countable family...

This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics related biological systems, that focus how small impacts can significantly change the state system at large spatial scales. problem is very extensive, it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons Schrodinger models DNA as examples self-organization molecular level, well examine features their...

The subspaces of Riemannian space signature (+---) that admit separation the Dirac equation have been found in case admitting Hamilton-Jacobi equation. For variables it is necessary for complete set Killing vectors and tensors to be a special kind. Every defines its own type metric which called Stackel space. does not permit general cases main idea paper construction, space, another This consists three matrix first-order differential symmetry operators are pairwise commuting linearly...

As reported in the literature, many investigations have been performed to provide a better understanding of two-phase heat transfer at microscale, which is very important electronics and optoelectronic components cooling by micro exchangers. However, these studies not yet led general conclusion. Recently Porous Media Laboratory (Minsk, Belarus) some experiments carried out investigation mini/microscale fluids (propane) flux ranges 102−105 W/m2. Experimental pool boiling evaporation mini...