相关论文: Dressing chain equations associated to difference …

The dressing chain is derived by applying Darboux transformations to the spectral problem of the Korteweg-de Vries (KdV) equation. It is also an auto-B\"acklund transformation for the modified KdV equation. We show that by applying Darboux…

We consider multilinear generalization of the Hirota derivative, which serves as a building block for integrable solitonic hierarchies. 2 special integrable mutlilinear equations are shown to be splittable into pairs of bilinear operators,…

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…

We review some of the fundamental notions associated to the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary…

We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko…

We study a simple nonlinear vector model defined on the honeycomb lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such…

Considering the coupled envelope equations in nonlinear couplers, the question of integrability is attempted. It is explicitly shown that Hirota's bilinear method is one of the simple and alternative techniques to Painlev\'e analysis to…

The soliton solutions of the Camassa-Holm equation are derived by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by other methods.

The dressing chain equations for the second order Sturm-Liouville differential operators is integrated. The simplest closure at the third step is linked to the spectral curve of the genus 1 and the explicit solution in elliptic Weierstrass…

Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…

Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…

Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral…

We present a new approach to determine the rational solutions of the higher order Painleve equations associated to periodic dressing chain systems. We obtain new sets of solutions, giving determinantal representations indexed by specific…

Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…

The $\dbar$-dressing scheme based on local nonlinear vector $\dbar$-problem is developed. It is applicable to multidimensional nonlinear equations for vector fields, and, after Hamiltonian reduction, to heavenly equation. Hamiltonian…

It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…

We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single…

We implement the dressing method for a novel integrable generalization of the nonlinear Schr\"odinger equation. As an application, explicit formulas for the $N$-soliton solutions are derived. As a by-product of the analysis, we find a…

It is shown that, by letting wavenumbers and frequencies complex in Hirota's bilinear method, new classes of exact solutions of soliton equations can be obtained systematically. They include not only singular or N-homoclinic solutions but…

Links of factorization theory, supersymmetry and Darboux transformations as isospectral deformations are considered in the context of quantum theory. The infinite chain equations for factorizing operators for a spectral problem are derived.…