In this paper, we introduce a modification of the Singular Manifold Method in order to derive associated spectral problem for generalization complex version modified Korteweg–de Vries equation. This yields right Lax pair and allows us implement binary Darboux transformations, which can be used construct an iterative method obtain exact solutions.

Recently, more and more data are published and exchanged by XML on the Internet. However, different XML data sources might contain the same data but have different structures. Therefore, it requires an efficient method to integrate such XML data sources so that more complete and useful information can be conveniently accessed and acquired by users. The tree edit distance is regarded as an effec...

We present, for the first time, two hierarchies of nonlinear, integrable q-difference equations, one of which includes a q-difference form of each of the second and fifth Painlevé equations, qPII and qPV, the other includes qPIII. All the equations have multiple free parameters. A method to calculate a 2× 2 Lax pair for each equation in the hierarchy is also given.

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented. PACS number: 02. 03. Ik

A vector asymmetrical Nizhnik–Novikov–Veselov (NNV) equation is proposed based on its bilinear form. Soliton solutions expressed by Pfaffians are obtained. Bilinear Bäcklund transformation and the corresponding Lax pair for the vector ANNV equation are derived. © 2008 Elsevier Inc. All rights reserved.

The main objectives of this work are to deduce the Lax pair for Modified Toda lattice hierarchy and find whether there exists a transformation between (2+1)-dimensional derivative equation equation. By new spectral problem, we obtain hierarchy, furthermore give Hirota’s form solution equation, thus can also be attained correspondingly.

In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M(Q) = i ( d dx Im −Q −Q − d dx Im ) , where Q represents a symmetric m × m matrix (i.e., Q(x) = Q(x) a.e.) with entries in L loc (R), is J -self-adjoint, where J is the antilinear conjugation defined by J = σ1C, σ1 = ( 0 Im Im 0 ) and C(a1, . . . , am, b1, . . . , bm) = (a1, . . . ,...