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We investigate the properties of nonlinear excitations in different types of soliton bearing systems with long-range dispersive interaction. We show that length-scale competition in such systems universally results in a multi-component…
We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- $\gtsl_{n+1}$-modules. The formulas are closely related to WZNW model at a…
We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a…
We developed a general framework for simulating multicomponent and multiphase systems using the lattice Boltzmann framework. Despite the fact that there is no restriction on the number of components in principle, in this article we focus an…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
We study monotone extension problems in the general framework of dual systems, without assuming separation. The paper develops a compact target-set formulation that includes multivalued operators as a special case and allows the initial set…
In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) Find a `Lax representation' where all the kinetic variables are combined into a single matrix $\rho$,…
We present exact multi-parameter families of soliton solutions for two- and three-component Manakov equations in the \emph{defocusing} regime. Existence diagrams for such solutions in the space of parameters are presented. Fundamental…
We consider the logarithmic Schr{\"o}dinger equation (logNLS) in the focusing regime. For this equation, Gaussian initial data remains Gaussian. In particular, the Gausson-a time-independent Gaussian function-is an orbitally stable…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
For the nonlinear Klein-Gordon equation in R 1+d , we prove the existence of multi-solitary waves made of any number N of decoupled bound states. This extends the work of C{\^o}te and Mu{\~n}oz (Forum Math. Sigma 2 (2014)) which was…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
In this paper, we propose a multi-component system of Camassa-Holm equation, denoted by CH($N$,$H$) with 2N components and an arbitrary smooth function $H$. This system is shown to admit Lax pair and infinitely many conservation laws. We…
The exponentially decreasing signal to noise ratio in multibaryon correlators is the main obstacle to a first principles, QCD-based calculation of the nuclear force. Recently, we have proposed an orbifold boundary condition ("restless…
In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…