Related papers: Abelian Toda solitons revisited
We find new solutions, including soliton-like ones, for a special case of non-Abelian loop Toda equations associated with complex general linear groups. We use the method of rational dressing based on an appropriate block-matrix…
We consider abelian twisted loop Toda equations associated with the complex general linear groups. The Dodd--Bullough--Mikhailov equation is a simplest particular case of the equations under consideration. We construct new soliton solutions…
We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation…
We present an elementary derivation of the soliton-like solutions in the $A_n^{(1)}$ Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are…
We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two…
Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely…
We analyze several types of soliton solutions to a family of Tzitzeica equations. To this end we use two methods for deriving the soliton solutions: the dressing method and Hirota method. The dressing method allows us to derive two types of…
We introduce the notion of abelian solutions of the 2D Toda lattice equations and the bilinear discrete Hirota equation and show that all of them are algebro-geometric.
In this talk we report some results about the construction of soliton solutions for the Affine and Conformal Affine Toda models using the Hirota's method. We obtain new classes of solitons connected to the degeneracies of the Cartan matrix…
A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons) in wronskian formare obtained using the method of Ablowitz and Satsuma. Also an…
Using Hirota's method, solitons are constructed for affine Toda field theories based on the simply-laced affine algebras. By considering automorphisms of the simply-laced Dynkin diagrams, solutions to the remaining algebras, twisted as well…
The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the "long wave" limit procedure of…
We study the relation between the group-algebraic approach and the dressing symmetry one to the soliton solutions of the $A_n^{(1)}$ Toda field theory in 1+1 dimensions. Originally solitons in the affine Toda models has been found by Olive,…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
In this paper, the classification in [Lin,Wei,Ye] of solutions to Toda systems of type $A$ with singular sources is generalized to Toda systems of types $C$ and $B$. Like in the $A$ case, the solution space is shown to be parametrized by…
We consider the Hirota equation (the discrete analog of the generalized Toda system) over a finite field. We present the general algebro-geometric method of construction of solutions of the equation. As an example we construct analogs of…
The soliton solutions of the Degasperis-Procesi equations are constructed by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by Hirota's method.
A simple procedure to enumerate all Toda systems associated with complex classical Lie groups is given.
We investigate existence of solitonic solutions for higher-order partial differential equations with polynomial nonlinearities. Using the Hirota method we obtain classification for higher-order integrable systems of equations.
We consider the soliton solutions in 1- and (1+1)-dimensional Toda lattice models with a boundary. We make use of the solutions already known on a full line by means of the Hirota's method. We explicitly construct the solutions satisfying…