Related papers: Completion of the integrable coupling systems

Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda…

We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both…

The reduction by restricting the spectral parameters $k$ and $k'$ on a generic algebraic curve of degree $\mathcal{N}$ is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable…

We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the…

Addition of higher nonlinear terms to the well known integrable nonlinear Schr\"odinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel…

We review our work on the relation between integrability and infinite-dimensional algebras. We first consider the question of what sets of commuting charges can be constructed from the current of a \mbox{\sf U}(1) Kac-Moody algebra. It…

A unifying scheme based on an ancestor model is proposed for generating a wide range of integrable discrete and continuum as well as inhomogeneous and hybrid models. They include in particular discrete versions of sine-Gordon,…

Recent concept of integrable nonholonomic deformation found for the KdV equation is extended to the mKdV equation and generalized to the AKNS system. For the deformed mKdV equation we find a matrix Lax pair, a novel two-fold integrable…

In this article we study an integrable deformation of the Kapustin-Witten equations. Using the Weyl-Wigner-Moyal-Groenewold description an integrable $\star$-deformation of a Kapustin-Witten system is obtained. Starting from known solutions…

We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…

Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0, 1,…

We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV…

In this paper we study certain aspects of the complete integrability of the Generalized Weierstrass system in the context of the Sinh-Gordon type equation. Using the conditional symmetry approach, we construct the B\"{a}cklund…

Standard (Arnold-Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones. Actually this…

A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by…

We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general $N$-component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat…

We introduce a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\times N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated discrete integrable systems. We present…

We construct a new class of N-dimensional Lie algebras and apply them to integrable systems. In this paper, we obtain a nonisospectral KdV integrable hierarchy by introducing a nonisospectral spectral problem. Then, a coupled nonisospectral…

The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this letter we deal with such a two-component integrable system of coupled…

We consider half-BPS Wilson loops in $\mathcal{N} = 2$ long circular quiver gauge theories at large-$N$ with continuous limit shape of 't Hooft couplings. In the limit of an infinite number of nodes $L$, the solution to the localisation…