Related papers: Nonlocal pseudosymmetries and B\"acklund transform…
Proper lattices for the discrete BKP and the discrete DKP equaitons are determined. Linear B\"acklund transformation equations for the discrete BKP and the DKP equations are constructed, which possesses the lattice symmetries and generate…
We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the "equations of motion" on the defect point via the space-like and time-like description. We then exploit the structural…
We discuss applications of the perturbative QCD approach in the exclusive non-leptonic two body B-meson decays. We briefly review its ingredients and some important theoretical issues on the factorization approaches. PQCD results are…
The new integrable mapping with a simple geometric interpretation is presented. This mapping arise from the nonlinear superposition principle for the B\"acklund transformations of some vector evolution equation.
We demonstrate how nonlocal regularization is applied to gauge invariant models with spontaneous symmetry breaking. Motivated by the ability to find a nonlocal BRST invariance that leads to the decoupling of longitudinal gauge bosons from…
We extend Painlev\'e IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlev\'e IV and II equations for special limits of the underlying…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
We investigate basic features of Bianchi's B\"acklund transformation of quadrics to see if it can be obtained under weaker assumptions and if it can be generalized to deformations of other surfaces.
Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.
This thesis examines the non-leptonic B-decays within QCD factorisation and beyond, to challenge the assumptions and limitations of the method. We analyse the treatment of the distribution amplitudes of light mesons and present a new model…
The B\"{a}cklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and…
We derive the quantum analogue of a B\"acklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schr\"odinger equation. The quantisation of the Ablowitz-Ladik chain leads to the $q$-boson model.…
For functions defined on C^n or (R_+)^n we construct a dequantization transform, which is closely related to the Maslov dequantization. The subdifferential at the origin of a dequantized polynomial coincides with its Newton polytope. For…
Following the work of Duistermaat-Singer \cite{DS} on isomorphisms of algebras of global pseudodifferential operators, we classify isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we…
We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe…
B\"acklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of B\"acklund transformations admitted by this equation are constructed. Schwartzian derivative as well as its invariance…
Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…
The nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations is considered. Formulae for the nonlocal Darboux transformation are obtained and its relation to the generalized Moutard…
This is a research announcement on what is best termed `nonlocal' methods in mathematics. (This is not to be confused with global analysis.) The nonlocal formulation of physics in \cite{principia} points to a fresh viewpoint in mathematics:…
It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…