Related papers: Bilinear Equations and B\"acklund Transformation f…
We propose an ultradiscrete analogue of Pl\"ucker relation specialized for soliton solutions. It is expressed by an ultradiscrete permanent which is obtained by ultradiscretizing the permanent, that is, the signature-free determinant. Using…
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…
We construct generalized solutions to the ultradiscrete KdV equation, including the so-called negative solition solutions. The method is based on the ultradiscretization of soliton solutions to the discrete KdV equation with gauge…
For a generalized super KdV equation, three Darboux transformations and the corresponding B\"acklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax…
We propose a new type of soliton equation, which is obtained from the generalized discrete BKP equation. The obtained equation admits two types of soliton solutions. The signs of amplitude and velocity of the soliton solution are opposite…
A q-discrete version of the two-dimensional Toda molecule equation is proposed through the direct method. Its solution, B\"acklund transformation and Lax pair are discussed. The reduction to the q-discrete cylindrical Toda molecule equation…
A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.
We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The…
The Baecklund transformation for the ultradiscrete KP equation is proposed. An algorithm to eliminate variables from the ultradiscrete linear equations is proposed. The consistency condition for the Baecklund transformation equations is…
In the paper we discuss the B\"acklund transformation of the KdV equation between solitons and solitons, between negatons and negatons, between positons and positons, between rational solution and rational solution, and between complexitons…
Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete…
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related…
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the $\tau$ function are presented. B\"acklund transformations of the…
We construct integrable discrete nonautonomous quad-equations as B\"acklund auto-transformations for known Volterra and Toda type semidiscrete equations, some of which are also nonautonomous. Additional examples of this kind are found by…
Binary symmetry constraints are applied to constructing B\"acklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville…
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…
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This…
By introducing generalized Backlund Transformations depending on arbitrary functions, wave and localized soliton solutions of the Davey- Stewartson equations are generated. Moreover explicit soliton solutions of the Hamiltonian DSI and…
We propose an ultradiscrete permanent solution to the ultradiscrete KP equation. The ultradiscrete permanent is an ultradiscrete analogue of the usual permanent. The elements on this ultradiscrete permanent solution are required some…
We will give a short introduction to discrete or lattice soliton equations, with the particular example of the Korteweg-de Vries as illustration. We will discuss briefly how B\"acklund transformations lead to equations that can be…