相关论文: B\"acklund transformations for fourth Painlev\'e h…
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
Backlund transformations are used to search for solutions, particularly soliton solutions, of non-linear differential equations. In this paper we present an invariant geometrical theory of Backlund transformations for second order evolution…
We begin by considering several properties commonly (but not universally) possessed by B\"acklund transformations between hyperbolic Monge-Amp\`ere equations: wavelike nature of the underlying equations, preservation of independent…
Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations ($RS$-transformations) are used to construct algebraic solutions of the sixth…
We introduce certain B\"acklund transformations for rational solutions of the Painlev\'e VI equation. These transformations act ona family of Painlev\'e VI tau functions. They are obtained from reducing the Hirota bilinear equations that…
We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlev\'{e} transcendents. The main results…
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…
In this work we show that, under certain conditions, parametric Backlund transformations (BTs) for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous…
The last decades saw growing interest across multiple disciplines in nonlinear phenomena described by partial differential equations (PDE). Integrability of such equations is tightly related with the Painleve property - solutions being free…
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…
In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e…
Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…
The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized…
A general theorem on the GBDT version of the B\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and…
We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in nonhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary…
We take a third-order approach to the fourth Painlev\'e equation and indicate the value of such an approach to other second-order ODEs in the Painlev\'e-Gambier list of 50.
The first, second and fourth Painlev\'{e} equations are studied by means of dynamical systems theory and three dimensional weighted projective spaces $\C P^3(p,q,r,s)$ with suitable weights $(p,q,r,s)$ determined by the Newton diagrams of…
We present a geometric construction of Backlund transformations and discretizations for a large class of algebraic completely integrable systems. To be more precise, we construct families of Backlund transformations, which are naturally…
The B\"acklund transformation (BT) for the "good" Boussinesq equation and its superposition principles are presented and applied. Unlike many other standard integrable equations, the Boussinesq equation does not have a strictly algebraic…
A seventh order ordinary differential equation (ODE) arising by reduction of the Drinfeld-Sokolov hierarchyis shown to be identical to a similarity reduction of an equationin the hierarchy of Sawada-Kotera.We also exhibit its link with a…