Journal of Nonlinear Mathematical Physics

Volume 22, Issue 3, June 2015

1. Corrigendum

Some remarks on materials with memory: heat conduction and viscoelasticity

Sandra Carillo
Pages: i - iii
Research Article

2. Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

Wei Fu, Zhijun Qiao, Junwei Sun, Da-jun Zhang
Pages: 321 - 341
In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem...
Research Article

3. Massey products, A-algebras, differential equations, and Chekanov homology

Lida Mendoza, Enrique G. Reyes
Pages: 342 - 360
We consider (classical and generalized) Massey products on the Chekanov homology of a Legendrian knot, and we prove that they are invariant under Legendrian isotopies. We also construct a minimal A∞-algebra structure on the Chekanov algebra of a Legendrian knot, we prove that this structure is invariant...
Research Article

4. A generalized Schrödinger equation via a complex Lagrangian of electrodynamics

Nicoleta Aldea, Gheorghe Munteanu
Pages: 361 - 373
In this paper we give a generalized form of the Schrödinger equation in the relativistic case, which contains a generalization of the Klein-Gordon equation. By complex Legendre transformation, the complex Lagrangian of electrodynamics produces a complex relativistic Hamiltonian H of electrodynamics,...
Letter to Editor

5. On some connections between the Gompertz function and special numbers

Grzegorz Rządkowski, Wojciech Rządkowski, Paweł Wójcicki
Pages: 374 - 380
In the present paper we show that the Gompertz function, the Fisher–Tippett and the Gumbel probability distributions are related to both Stirling numbers of the second kind and Bernoulli numbers. Especially we prove for the Gumbel probability density function an analog of the Grosset–Veselov formula...
Research Article

6. Products of distributions and collision of a δ-wave with a δ′-wave in a turbulent model

C.O.R. Sarrico, A. Paiva
Pages: 381 - 394
We study the possibility of collision of a δ-wave with a stationary δ′-wave in a model ruled by equation f (t)ut+[u2−β(x−γ(t))u]x = 0, where f, β and γ are given real functions and u = u(x, t) is the state variable. We adopt a solution concept which is a consistent extension of the classical solution...
Research Article

7. Algebro-geometric Constructions of Quasi Periodic Flows of the Discrete Self-dual Network Hierarchy and Applications

Dong Gong, Xianguo Geng
Pages: 395 - 427
In this paper we obtain the discrete integrable self-dual network hierarchy associated with a discrete spectral problem. On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the discrete self-dual network hierarchy are straightened using the Abel-Jacobi coordinates....
Research Article

8. Magnetic curves in Sasakian manifolds

Simona Luiza Druţă-Romaniuc, Jun-ichi Inoguchi, Marian Ioan Munteanu, Ana Irina Nistor
Pages: 428 - 447
In this paper we classify the magnetic trajectories corresponding to contact magnetic fields in Sasakian manifolds of arbitrary dimension. Moreover, when the ambient is a Sasakian space form, we prove that the codimension of the curve may be reduced to 2. This means that the magnetic curve lies on a...
Research Article

9. Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation

Spyridon Kamvissis, Dmitry Shepelsky, Lech Zielinski
Pages: 448 - 473
We consider the initial boundary value (IBV) problem for the focusing nonlinear Schrödinger equation in the quarter plane x>0, t >0 in the case of periodic initial data, u(x,0) = α exp(−2iβx) (or asymptotically periodic, u(x, 0) =α exp(−2iβx)→0 as x→∞), and a Robin boundary condition at x = 0:...