Journal of Nonlinear Mathematical Physics

Volume 26, Issue 3, May 2019
Letter to Editor

1. A Note on the Equivalence of Methods to finding Nonclassical Determining Equations

J. Goard
Pages: 327 - 332
In this note we prove that the method of Bîlã and Niesen to determine nonclassical determining equations is equivalent to that of Nucci’s method with heir-equations and thus in general is equivalent to using an appropriate form of generalised conditional symmetry.
Research Article

2. Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

Rustem N. Garifullin, Giorgio Gubbiotti, Ravil I. Yamilov
Pages: 333 - 357
In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous...
Research Article

3. Search for CAC-integrable homogeneous quadratic triplets of quad equations and their classification by BT and Lax

Jarmo Hietarinta
Pages: 358 - 389
We consider two-dimensional lattice equations defined on an elementary square of the Cartesian lattice and depending on the variables at the corners of the quadrilateral. For such equations the property often associated with integrability is that of “multidimensional consistency” (MDC): it should be...
Research Article

4. Two-component generalizations of the Novikov equation

Hongmin Li
Pages: 390 - 403
Some two-component generalizations of the Novikov equation, except the Geng-Xue equation, are presented, as well as their Lax pairs and bi-Hamiltonian structures. Furthermore, we study the Hamiltonians of the Geng-Xue equation and discuss the homogeneous and local properties of them.
Research Article

5. Bilinear Identities and Squared Eigenfunction Symmetries of the BCr-KP Hierarchy

Lumin Geng, Huizhan Chen, Na Li, Jipeng Cheng
Pages: 404 - 419
The BCr-KP hierarchy is an important sub hierarchy of the KP hierarchy, which includes the BKP and CKP hierarchies as the special cases. Some properties of the BCr-KP hierarchy and its constrained case are investigated in this paper, including bilinear identities and squared eigenfunction symmetries....
Research Article

6. Products in the category of 𝕑2n-manifolds

Andrew Bruce, Norbert Poncin
Pages: 420 - 453
We prove that the category of 𝕑2n-manifolds has all finite products. Further, we show that a 𝕑2n-manifold (resp., a 𝕑2n-morphism) can be reconstructed from its algebra of global 𝕑2n-functions (resp., from its algebra morphism between global 𝕑2n-function algebras). These results are of importance...
Research Article

7. Integration of the stochastic logistic equation via symmetry analysis

Giuseppe Gaeta
Pages: 454 - 467
We apply the recently developed theory of symmetry of stochastic differential equations to a stochastic version of the logistic equation, obtaining an explicit integration, i.e. an explicit formula for the process in terms of any single realization of the driving Wiener process.
Research Article

8. Quasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy

Peng Zhao, Engui Fan, Temuerchaolu
Pages: 468 - 482
We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebrogeometric method. Our main tools include algebraic curve and Riemann surface, polynomial recursive formulation and a special meromorphic function.
Research Article

9. The Riemann–Hilbert problem to coupled nonlinear Schrödinger equation: Long-time dynamics on the half-line

Boling Guo, Nan Liu
Pages: 483 - 508
We derive the long-time asymptotics for the solution of initial-boundary value problem of coupled nonlinear Schrödinger equation whose Lax pair involves 3 × 3 matrix in present paper. Based on a nonlinear steepest descent analysis of an associated 3 × 3 matrix Riemann–Hilbert problem, we can give the...