Related papers: Higher-order solitons in the N-wave system
The self-organization processes of nanopattern formation on semiconductor surfaces under low energy ion beam bombardment is considered. The new mathematical model based on nonlinear evolution equation of the sixth order is presented. The…
This paper is devoted to the study of solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions…
The scattering of charged solitons in the complex sine-Gordon field theory is investigated. An exact factorizable S-matrix for the theory is proposed when the renormalized coupling constant takes the values $\lambda^{2}_{R}=4\pi/k$ for any…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A soliton is a solitary wave which exhibits some strong form of stability so that…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an Nth-order…
The model of laminated wave turbulence puts forth a novel computational problem - construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order $10^{12}$ and more. The equations to be solved in…
A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the…
Building on [1], we examine a holographic model in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. The symmetry breaking is realized through the St\"{u}ckelberg mechanism, and leads to a scalar…
We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We…
This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution…
We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence non-St\"ackel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the…
We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation…
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…
The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem. We show how the second order reductions of the N-wave…
Whether monochromatic, pulsed, or even constant and crossed, the field used to describe the interaction of charged fermions with an intense laser beam is mainly assumed to be of plane-wave form. We consider a simple extension to plane-wave…
The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of…
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 four-wave mixing Hamiltonian system on the classical as well as on the quantum level is investigated. In the classical case, if one assumes the frequency resonance condition of the form $\omega_0 -\omega_1 +\omega_2 -\omega_3=0$, this…