Related papers: Lump type solutions: Backlund transformation and s…
We propose a novel method for establishing the convergence rates of solutions to reaction-diffusion equations to traveling waves. The analysis is based on the study of the traveling wave shape defect function introduced in [2]. It turns out…
Treating an integrable quad-equation along with its two generalised symmetries as a compatible system allows one to construct an auto-B\"acklund transformation for solutions of the related NLS-type system. A fixed periodic reduction of the…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…
Let $q(x,y)$ be an nondegenerate lump solution to KP-I (Kadomtsev-Petviashvili-I) equation $$\partial_x^4q-2\sqrt{2}\partial_x^2q-3\sqrt{2}\partial_x((\partial_xq) ^2)-2\partial_y^2q=0. $$ We prove the existence of a traveling wave solution…
The Backlund transformation related symmetry is nonlocal, which is hardly to apply in constructing solutions for nonlinear equations. In this paper, we first localize nonlocal residual symmetry to Lie point symmetry by introducing multiple…
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the $\tau$ function are presented. B\"acklund transformations of the…
Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation…
We prove that if a solution of an equation of KdV type is bounded above by a traveling wave with an amplitude that decays faster than a given linear exponential then it must be zero. We assume no restrictions neither on the size nor in the…
We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of…
We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy…
We present an interpolative method for describing coherent transport through an interacting quantum dot. The idea of the method is to construct an approximate electron self-energy which becomes exact both in the limits of weak and strong…
We use blow-up solutions of nonlinear Helmholtz equations to introduce a nonlinear resonance effect that is capable of amplifying electromagnetic waves of particular intensity. To achieve this, we propose a scattering setup consisting of a…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
In this paper, two types of traveling wave solutions to the osmosis K(2, 2) equation are investigated. They are characterized by two parameters. The expresssions for the soliton and periodic wave solutions are obtained.
Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is…
A multiscale approach was adopted for the calculation of confined states in self-assembled semiconductor quantum dots (QDs). While results close to experimental data have been obtained with a combination of atomistic strain and…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
In this paper we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic-quintic Ginzburg-Landau equation. The primary tools used here are Hopf…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…