Related papers: Addition formulae, B\"acklund transformations, per…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
We apply the GBDT version of the B\"acklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular $m_1 \times m_2$ matrix functions are dealt with.…
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson…
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
In this paper, we derive a B\"{a}cklund transformation for the supersymmetric Kortweg-de Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the…
The permutability of two Backlund transformations is employed to construct a non linear superposition formula and to generate a class of solutions for the N=2 super sine-Gordon model.
A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of…
In this paper, we define the modified formal variable separation approach and show how it determines, in a remarkably simple manner, the decomposition solutions, the B\"acklund transformations, the Lax pair, and the linear superposition…
The bilinear equations of the $N$-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main…
By using B\"acklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation $ z_{yy} + ({1}/{z})_{xx} + 2 = 0 $ are generated from a seed which corresponds to Lipschitz surfaces of…
A continuous solution of an algebraic equation with holomorphic almost periodic coefficients is also almost periodic.
We introduce a parametric coupled KdV system which contains, for particular values of the parameter, the complex extension of the KdV equation and one of the Hirota-Satsuma integrable systems. We obtain a generalized Gardner transformation…
We consider the hyperbolic generalization of Burgers equation with polynomial source term. The transformation of auto-B\"{a}cklund type was found. Application of the results is shown in the examples, where the pair of two stationary…
Adapting Lindstr\"om's well-known construction, we consider a wide class of functions which are generated by flows in a planar acyclic directed graph whose vertices (or edges) take weights in an arbitrary commutative semiring. We give a…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
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.
We present improved Coulomb correction formulae for Bose-Einstein correlations including also exchange term and use them to calculate appropriate correction factors for several source functions. It is found that Coulomb correction to the…
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…
We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…