Related papers: Invariance of the Kaup-Kupershmidt equation and tr…
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…
A set of infinitely many nonlocal conservation laws are revealed for (1+1)-dimensional evolution equations. For some special known integrable systems, say, the KdV and Dym equations, it is found that different nonlocal conservation laws can…
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…
Chapter 4 of my book [1] is dedicated to Lie-B\"acklund group analysis of various types of differential equations. The Russian edition of this book had an Addendum (pages 262-266) containing a summary of new results (obtained by the end of…
The B\"acklund transformation and its nonlinear superposition principle are presented for the Krichever-Novikov equation $u_t= u_{xxx} - {3/(2u_x)} (u^2_{xx} - r(u)) + cu_x, r^{(5)}=0$.
In this paper, we obtained the non-local residual symmetry related to truncated Painlev\'e expansion of Burgers equation. In order to localize the residual symmetry, we introduced new variables to prolong the original Burgers equation into…
Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations. These links can be depicted in a…
We provide the B\"{a}cklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center. These are found explicitly. can be iterated via the Bianchi Permutability Theorem and can be further…
Using gauge transformations for the corresponding generating pseudo-differential operators $L^n$ in terms of eigenfunctions and adjoint eigenfunctions, we construct several types of auto-B\"{a}cklund transformations for the KP hierarchy…
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 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…
The $N=2 \;a=-2$ supersymmetric KdV equation is studied. A Darboux transformation and the corresponding B\"acklund transformation are constructed for this equation. Also, a nonlinear superposition formula is worked out for the associated…
This article encloses the derivation of Darboux solutions for Kaup Kupershmidt equations with their generalization in determinantal form. One of the main focuses of this work is to construct the Backlund transformation for the different…
We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this…
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…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under…
This is a continuation of hep-th/9811108, hep-th/9903218, hep-th/9910235, on exact integration technics for modified dynamical equations in ten dimensional supersymmetric gauge theory. A B\"acklund transformation is derived for the Yang…
We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this…
We apply the method of B\"acklund transformations to generate a new hierarchy of exact solutions to the vacuum Einstein equations starting from the extreme Kerr near-horizon geometry. Solutions with extreme Kerr near-horizon asymptotics…