Related papers: Generalized Heisenberg Ferromagnet type Equation a…
We study nonlocal reductions of coupled equations in $1+1$ dimensions of the Heisenberg ferromagnet type. The equations under consideration are completely integrable and have a Lax pair related to a linear bundle in pole gauge. We describe…
The gauge equivalence between the (2+1)-dimensional Zakharov equations and (2+1)-dimensional integrable continuous Heisenberg ferromagnetic model is established. Also their integrable reductions are shown explicitly.
The paper is dedicated to a system of matrix nonlinear evolution equations related to a Hermitian symmetric space of the type $\mathbf{A.III}$. The system under consideration extends the $1+1$ dimensional Heisenberg ferromagnet equation in…
We generalize the integrable Heisenberg ferromagnet model according to each Hermitian symmetric spaces and address various new aspects of the generalized model. Using the first order formalism of generalized spins which are defined on the…
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…
A generalized Toda Lattice equation is considered. The associated linear problem (Lax representation) is found. For simple case N=3 the $\tau$-function Hirota form is presented that allows to construct an exast solutions of the equations of…
We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times…
It is shown that the generalized Riemann equation is equivalent with the multicomponent generalization of the Hunter - Saxton equation. New matrix and scalar Lax representation is presented for this generalization. New class of the…
This paper aims at providing an exact algebro-geometric solution of the modified Camassa-Holm (mCH) equation derived from hyperelliptic curves in $4(p+q)-1$ genus. To achieve this goal, we construct the Riemann-Hilbert problems cosponsoring…
We present in this report 1+1 dimensional nonlinear partial differential equation integrable through inverse scattering transform. The integrable system under consideration is a pseudo-Hermitian reduction of a matrix generalization of…
In this paper we present a general vacuum solution of the modified Gauss-Bonnet gravity equations for the Friedmann-Lema\^itre-Robertson-Walker metric. We use an ansatz to reduce the gravitational equations to an ordinary differential…
The non-topological, stationary and propagating, soliton solutions of the classical continuous Heisenberg ferromagnet equation are investigated. A general, rigorous formulation of the Inverse Scattering Transform for this equation is…
Higher flows of the Heisenberg ferromagnet equation and the Wadati-Konno-Ichikawa equation are generalized into multi-component systems on the basis of the Lax formulation. It is shown that there is a correspondence between the…
This paper is a continuation of our previous work in which we studied a sl(3) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the integrable hierarchy of nonlinear evolution equations associated with it.…
In this work, the generalized $N$-component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for $N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main purpose of…
We extend previous work [Y. E. Litvinenko, Phys. Plasmas 17, 074502 (2010)] on a direct method for finding similarity reductions of partial differential equations such as the Grad-Shafranov equation, to the case of the generalized…
The full Landau-Lifshitz-Gilbert equation with periodic material coefficients and natural boundary condition is employed to model the magnetization dynamics in composite ferromagnets. In this work, we establish the convergence between the…
This paper examines a generalization of the Camassa-Holm equation from the perspective of integrability. Using the framework developed by Dubrovin on bi-Hamiltonian deformations and the general theory of quasi-integrability, we demonstrate…
We introduce a class of equivalences, which we call generalized semi-infinite Hecke equivalences, between certain categories of representations of graded associative algebras which appear in the setting of semi-infinite cohomology for…
The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…