Journal of Nonlinear Mathematical Physics

Volume 19, Issue 3, September 2012
Letter to Editor

1. Invariance of the Kaup–Kupershmidt Equation and Triangular Auto-Bäcklund Transformations

Marianna Euler, Norbert Euler
Pages: 285 - 291
We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup–Kupershmidt equation derived by E. G. Reyes in his paper titled “Nonlocal symmetries and the Kaup–Kupershmidt equation” [J. Math. Phys....
Letter to Editor

2. Conservation Laws for the Schrödinger–Newton Equations

G. Gubbiotti, M. C. Nucci
Pages: 292 - 299
In this Letter a first-order Lagrangian for the Schrödinger–Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 4844–4877]. Then Noether's theorem is applied to the Lie point symmetries determined...
Research Article

3. Billiard Algebra, Integrable Line Congruences, and Double Reflection Nets

Vladimir Dragović, Milena Radnović
Pages: 300 - 317
Billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the operational consistency for the billiard algebra, is equivalent to an integrability...
Research Article

4. The First Cohomology of the Superconformal Algebra K(1|4)

Elena Poletaeva
Pages: 318 - 329
The infinitesimal deformations of the embedding of the Lie superalgebra of contact vector fields on the supercircle S1|4 into the Poisson superalgebra of symbols of pseudodifferential operators on S1|2 are explicitly calculated.
Research Article

5. Lagrangians for Biological Models

M. C. Nucci, K. M. Tamizhmani
Pages: 330 - 352
We show that a method presented in [S. L. Trubatch and A. Franco, Canonical Procedures for Population Dynamics, J. Theor. Biol. 48 (1974) 299–324] and later in [G. H. Paine, The development of Lagrangians for biological models, Bull. Math. Biol. 44 (1982) 749–760] for finding Lagrangians of classic models...
Research Article

6. Functional Representation of the Negative AKNS Hierarchy

V. E. Vekslerchik
Pages: 353 - 372
This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's...
Research Article

7. Geometry of the Recursion Operators for the GMV System

A. B. Yanovski, G. Vilasi
Pages: 373 - 390
We consider the Recursion Operator approach to the soliton equations related to a auxiliary linear system introduced recently by Gerdjikov, Mikhailov and Valchev (GMV system) and their interpretation as dual of Nijenhuis tensors on the manifold of potentials.
Research Article

8. Laplace Invariants for General Hyperbolic Systems

Chris Athorne, Halis Yilmaz
Pages: 391 - 410
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
Research Article

9. On the Nonlocal Symmetries of the μ-Camassa–Holm Equation

Ognyan Christov
Pages: 411 - 427
The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm and the Hunter–Saxton equations. This equation admits quadratic pseudo-potentials which allow us to compute some first-order nonlocal symmetries. The found symmetries preserve...
Research Article

10. Spectral Zeta Functions of a 1D Schrödinger Problem

Joe Watkins
Pages: 428 - 444
We study the spectral zeta functions associated to the radial Schrödinger problem with potential V(x) = x2M + αxM−1 + (λ2 − 1/4)/x2. After directly computing some of the zeta functions, we use the quantum Wronskian equation to give sum rules between them, allowing for instances where the explicit form...