Related papers: Darboux Transformations for Supersymmetric Kortewe…
In this paper, we propose a new approach to calculate multi-soliton solutions of Camassa-Holm (CH) equation and modified Camassa-Holm (MCH) equation with aid of Darboux transformation (DT). The new approach simplifies the approach presented…
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux…
The n-fold Darboux transformation (DT) is a 2\times2 matrix for the Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed by a ratio of $(n+1)\times (n+1)$ determinant and $n\times n$ determinant of eigenfunctions.…
For eleven examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux-Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be equivalent to Krein-Adler transformations…
The N=1 supersymmetric modified Korteweg-de Vries (SmKdV) system is transformed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV (BSmKdV) passes the Painlev\'{e} test and allows a set of…
This paper is devoted to the systematic study of additional (non- isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type- the so called SKP_(R;M_B,M_F) models. The latter are supersymmetric…
We establish a correspondence between Darboux's special isothermic surfaces of type (A,0,C,D) and the solutions of the second order PDE : u\Delta(u)-|\nabla(u)|^{2}+\Phi^{4}=s, s \in R. We then use the classical Darboux transformation for…
It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using…
In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical…
Dark equations are defined as some kinds of integrable couplings with some fields being homogeneously and linearly coupled to others. In this paper, dark equations are extended in several aspects. Taking the Korteweg-de Vrise (KdV) equation…
The general approach to chain equations derivation for the function generated by a Miura transformation analog is developing to account evolution (second Lax equation) and illustrated for Sturm-Liouville differential and difference…
We construct a Backlund transformation for the trigonometric classical Gaudin magnet starting from the Lax representation of the model. The Darboux dressing matrix obtained depends just on one set of variables because of the so-called…
The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on some non-abelian Lie group, is studied and the solutions are shown to be expressed in terms of quasideterminants. As an…
We show that the auto-Backlund transformations of the sine-Gordon, Korteweg-deVries, nonlinear Schrodinger, and Ernst equations are related to their respective CPT symmetries. This is shown by applying the CPT symmetries of these equations…
We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We…
Using the group-theoretical approach to the inverse scattering method the supersymmetric Korteweg-de Vries equation is obtained by application of the Drinfeld-Sokolov reduction to osp(1|2) loop superalgebra. The direct and inverse…
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the…
We propose a discrete Darboux-Lax scheme for deriving auto-B\"acklund transformations and constructing solutions to quad-graph equations that do not necessarily possess the 3D consistency property. As an illustrative example we use the…
Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of nonisospectral equations were constructed using the GBDT version…
We present a new approach to the construction of the Darboux matrix. This is a generalization of the recently formulated method based on the assumption that the square of the Darboux matrix vanishes for some values of the spectral…