The (2+1)-dimensional Davey-Stewartson-like equations with variable coefficients have the applications in ultra-relativistic degenerate dense plasmas and Bose-Einstein condensates. Via Bell polynomials symbolic computation, bilinear form, Backlund transformation Lax pair for such are obtained. Based on Hirota method, we construct soliton solutions, analyze elastic collisions constant coefficien...

A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons)in wronskian form are obtained using the method of Ablowitz and Satsuma. Also an extended class of rational solutions are found using an appropriate recursion relation. They are also solutions of Boussinesq equation and it is conjectured that t...

We derive a generalization of the flat space Yang's and Newman's equations for self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian 4-manifolds. The results also apply Einstein metrics (whose full curvature is not necessarily self-dual). analyse possibility hidden symmetries in form Backlund transformations, we find continuous group only case which geometry half-flat. No isome...

Any locally invertible morphism of a finite-order jet space is either prolonged point transformation or Lie's contact (the Lie–Backlund theorem). We recall this classical result with simple proof and moreover determine explicit formulae even for all (not necessarily invertible) morphisms spaces. Examples generalized (higher-order) transformations jets that destroy subspaces are stated comments.

We discuss the non–autonomous nonlinear partial difference equations belonging to Boll classi?cation of quad graph consistent around cube. show how starting from compatible on a cell we can construct lattice equations, its Backlund transformations and Lax pairs. By carrying out algebraic entropy calculations that H4 trapezoidal H6 families are linearizable in few examples effectively linearize ...