Related papers: B\"acklund transformation for integrable systems
We study the integral transform which appeared in a different form in Akhiezer's textbook "Lectures on Integral Transforms".
The construction of type II Backlund transformation for the sine-Gordon and the Tzitzeica-Bullough-Dodd models are obtained from gauge transformation. An infinite number of conserved quantities are constructed from the defect matrices. This…
Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the von Mises transformation, with the unknown function taken as the new independent variable and an appropriate partial…
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
N-fold B\"acklund transformation for the Davey-Stewartson equation is constructed by using the analytic structure of the Lax eigenfunction in the complex eigenvalue plane. Explicit formulae can be obtained for a specified value of N. Lastly…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
Arguments are presented to show that in the case of entangled systems there are certain difficulties in implementing the usual Bohmian interpretation of the wave function in a straightforward manner. Specific examples are given.
We summarize the results of our recent work on B\"acklund transformations (BTs), particularly focusing on the relationship of BTs and infinitesimal symmetries. We present a BT for an associated Degasperis-Procesi (aDP) equation and its…
In a recent paper we presented a truncation-type method of deriving Backlund transformations for ordinary differential equations. This method is based on a consideration of truncation as a mapping that preserves the locations of a natural…
The permutability of two Backlund transformations is employed to construct a non linear superposition formula to generate a class of solutions for the N=1 super sinh-Gordon model.
This work focuses on two notions of non-Hamiltonian integrable systems: B-integrability and Euler-Jacobi integrability. We first show that the first notion is stronger. We then investigate which possible "non-evident" properties one can add…
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…
Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.
It is proved that for a given truncated Painlev\'e expansion of an arbitrary nonlinear Painlev\'e integrable system, the residue with respect to the singularity manifold is a nonlocal symmetry. The residual symmetries can be localized to…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…
Starting from nonlocal symmetries related to B\"acklund transformation (BT), many interesting results can be obtained. Taking the well known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in elegant and compact…
It is shown that B\"acklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry…
In this paper we introduce a variant of Burkholder's martingale transform associated with two martingales with respect to different filtrations. Even though the classical martingale techniques cannot be applied, we show that the discussed…
Consider the statement "Every Yang-Baxter integrable system is defined to be exactly-solvable". To formalise this statement, definitions and axioms are introduced. Then, using a specific Yang-Baxter integrable bosonic system, it is shown…