Erratum to: Virasoro and KdV

From Toda to KdV

For periodic Toda chains with a large number N of particles we consider states which are N−2-close to the equilibrium and constructed by discretizing arbitrary given C2−functions with mesh size N−1. Our aim is to describe the spectrum of the Jacobi matrices LN appearing in the Lax pair formulation of the dynamics of these states as N → ∞. To this end we construct two Hill operators H± – such op...

Erratum to: Armentum: a hybrid direct search optimization methodology

In the original publication of this article unfortunately the co-authors were omitted. The two co-authors are displayed now.

Erratum

Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...