Related papers: Solving non-abelian loop Toda equations
We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions…
We study a fully noncommutative generalisation of the commutative fourth Painlev\'e equation that possesses solutions in terms of an infinite Toda system over an associative unital division ring equipped by a derivation.
We consider an integrable conformally invariant two dimensional model associated to the affine Kac-Moody algebra SL(3). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor…
Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the…
We implement the dressing method for a novel integrable generalization of the nonlinear Schr\"odinger equation. As an application, explicit formulas for the $N$-soliton solutions are derived. As a by-product of the analysis, we find a…
We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra, Toda lattice, and sine-Gordon equations and their multi-soliton solutions.…
Due to higher-order Kaup-Newell (KN) system has more complex and diverse solutions than classical second-order flow KN system, the research on it has attracted more and more attention. In this paper, we consider a higher-order KN equation…
We restrict affine Toda field theory to the half-line by imposing certain boundary conditions at $x=0$. The resulting theory possesses the same spectrum of solitons and breathers as affine Toda theory on the whole line. The classical…
In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one…
The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a…
On the example of nonabelian Toda type theory associated with the Lie superalgebra $osp(2|4)$ we show that this integrable dynamical system is relevant to a black hole background metric in the corresponding target space. In the even sector…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its…
The nonlinear Dirac equation for Bose-Einstein condensates in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic…
We define an integrable hamiltonian system of Toda type associated with the real Lie algebra $\so{p}{q}$. As usual there exists a periodic and a non-periodic version. We construct, using the root space, two Lax pair representations and the…
We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution…
The asymptotic regimes of the N-site complex Toda chain (CTC) with fixed ends related to the classical series of simple Lie algebras are classified. It is shown that the CTC models have much richer variety of asymptotic regimes than the…
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…
Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda…
Exact solutions to the quantum S-matrices for solitons in simply-laced affine Toda field theories are obtained, except for certain factors of simple type which remain undetermined in some cases. These are found by postulating solutions…