Journal of Nonlinear Mathematical Physics

Volume 16, Issue 2, June 2009
Research Article

1. A Note on Traveling Wave Solutions to the Two Component Camassa–Holm Equation

Keivan Mohajer
Pages: 117 - 125
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa–Holm equation are distributional traveling wave solutions to the Camassa–Holm equation provided that the set u-1(c), where c is the speed of the wave, is of measure zero. In...
Research Article

2. Solutions of the Extended Kadomtsev–Petviashvili–Boussinesq Equation by the Hirota Direct Method

Asli Pekcan
Pages: 127 - 139
We show that we can apply the Hirota direct method to some non-integrable equations. For this purpose, we consider the extended Kadomtsev–Petviashvili–Boussinesq (eKPBo) equation with M variable which is (uxxx−6uux)x+a11uxx+2∑k=2Ma1kuxxk+∑i,j=2Maijuxixj=0, where aij = aji are constants and xi = (x,...
Research Article


M. Mansour
Pages: 141 - 150
In this paper, we introduce a q-analogue of the Tricomi expansion for the incomplete q-gamma function. A general method is described for converting a power series into an expansion in incomplete q-gamma function. Also, we use the q-Tricomi expansion for giving a formal proof of the relation between the...
Research Article

4. An Approximation of the Kinetic Energy of a Superfluid Film on a Riemann Surface

Chris Petersen Black
Pages: 151 - 160
The flow of a superfluid film adsorbed on a porous medium can be modeled by a meromorphic differential on a Riemann surface of high genus. In this paper, we define the mixed Hodge metric of meromorphic differentials on a Riemann surface and justify using this metric to approximate the kinetic energy...
Research Article

5. On Geodesic Completeness of Nondegenerate Submanifolds in Semi-Euclidean Spaces

Fazilet Erkekog˜lu
Pages: 161 - 168
In this paper, we study the geodesic completeness of nondegenerate submanifolds in semi-Euclidean spaces by extending the study of Beem and Ehrlich [1] to semi-Euclidean spaces. From the physical point of view, this extend may have a significance that a semi-Euclidean space contains more variety of Lorentzian...
Research Article

6. Commutativity of Pfaffianization and Bäcklund Transformations: The Leznov Lattice

Chun-Xia Li, Jun-Xiao Zhao, Xing-Biao Hu
Pages: 169 - 178
In this paper, we first obtain Wronskian solutions to the Bäcklund transformation of the Leznov lattice and then derive the coupled system for the Bäcklund transformation through Pfaffianization. It is shown the coupled system is nothing but the Bäcklund transformation for the coupled Leznov lattice...
Research Article

7. Solutions of the (2 + 1)-Dimensional KP, SK and KK Equations Generated by Gauge Transformations from Nonzero Seeds

Jingsong He, Xiaodong Li
Pages: 179 - 194
By using gauge transformations, we manage to obtain new solutions of (2 + 1)-dimensional Kadomtsev–Petviashvili (KP), Kaup–Kuperschmidt (KK) and Sawada–Kotera (SK) equations from nonzero seeds. For each of the preceding equations, a Galilean type transformation between these solutions u2 and the previously...
Research Article

8. A PDE Approach to Finite Time Indicators in Ergodic Theory

Olga Bernardi, Franco Cardin, Massimiliano Guzzo, Lorenzo Zanelli
Pages: 195 - 206
For dynamical systems defined by vector fields over a compact invariant set, we introduce a new class of approximated first integrals based on finite time averages and satisfying an explicit first order partial differential equation. These approximated first integrals can be used as finite time indicators...
Research Article

9. The Nonlinear Schrödinger Equation for the Delta-Comb Potential: Quasi-Classical Chaos and Bifurcations of Periodic Stationary Solutions

D. Witthaut, K. Rapedius, H. J. Korsch
Pages: 207 - 233
The nonlinear Schrödinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schrödinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight...
Research Article

10. Lepage Equivalents of Second-Order Euler–Lagrange Forms and the Inverse Problem of the Calculus of Variations

Olga Krupková, Dana Smetanová
Pages: 235 - 250
In the calculus of variations, Lepage (n + 1)-forms are closed differential forms, representing Euler–Lagrange equations. They are fundamental for investigation of variational equations by means of exterior differential systems methods, with important applications in Hamilton and Hamilton–Jacobi theory...