Journal of Nonlinear Mathematical Physics

Volume 18, Issue 4, December 2011
Letter to Editor

1. The Transformation between the AKNS Hierarchy and the KN Hierarchy with Self-Consistent Sources

Qi Li, Wen Zhang, Qiu-Yuan Duan, Deng-Yuan Chen
Pages: 483 - 490
It is shown that the AKNS hierarchy with self-consistent sources can transform to KN hierarchy with self-consistent sources through a transformation operator and gauge transformation. Besides, there exists transformation in their conservation laws and Hamiltonian structures.
Research Article

2. Propagation of Spikes in Nonresonant Atomic Media: The Reduced Maxwell-Duffing Model

Utpal Roy, Thokala Soloman Raju, Prasanta K. Panigrahi, Ashutosh Rai
Pages: 491 - 499
We obtain spikes or extremely short pulses for reduced Maxwell-Duffing equations under a general boundary condition, connecting the electric field and electron amplitude, using a Möbius transformation. For a nonzero background, this system is shown to admit two families of exact solutions in the form...
Research Article

3. New Integrable Multicomponent Nonlinear Partial Differential-Difference Equations

R. Sahadevan, S. Balakrishnan
Pages: 501 - 518
We report a new three and four coupled nonlinear partial differential-difference equations each admits Lax representation, possess infinitely many generalized (nonpoint) symmetries, conserved quantities and a recursion operator. Hence they are completely integrable both in the sense of Lax and Liouville.
Research Article

4. Generalization of an Invertible Transformation and Examples of its Applications

M. Bruschi, F. Calogero, F. Leyvraz, M. Sommacal
Pages: 519 - 540
Recently we highlighted the remarkable nature of an explicitly invertible transformation, we reported some generalizations of it and examples of its expediency in several mathematical contexts: algebraic and Diophantine equations, dynamical systems (with continuous and discrete time), nonlinear PDEs,...
Research Article

5. On a Periodic 2-Component Camassa–Holm Equation with Vorticity

Qiaoyi Hu
Pages: 541 - 556
We consider a periodic 2-component Camassa–Holm equation with vorticity in the paper. We first give the local well-posedness and the blow-up criterion for strong solutions to the equation in the Sobolev space Hs, s>32 . We then present a global existence result for strong solutions to the equation....
Research Article

6. Binary Darboux Transformation for the Supersymmetric Principal Chiral Field Model

Bushra Haider, M. Hassan
Pages: 557 - 581
The standard binary Darboux transformation is investigated and is used to obtain quasideterminant multisoliton solutions of the supersymmetric chiral field model in two dimensions.
Research Article

7. Laplace Transformation of Lie Class ω = 1 Overdetermined Systems

Boris Kruglikov
Pages: 583 - 611
In this paper, we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on one function of one variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration...
Research Article

8. Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant

Vera V. Kartak
Pages: 613 - 640
Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the examples the equivalence problem for the Painleve II equation, Painleve III...