Journal of Nonlinear Mathematical Physics

Volume 27, Issue 3, May 2020
Research Article

1. Elastic null curve flows, nonlinear C-integrable systems, and geometric realization of Cole-Hopf transformations

Zühal Küçükarslan Yüzbaşı, Stephen C. Anco
Pages: 357 - 392
Elastic (stretching) flows of null curves are studied in three-dimensional Minkowski space. As a main tool, a natural type of moving frame for null curves is introduced, without use of the pseudo-arclength. This new frame is related to a Frenet null frame by a gauge transformation that belongs to the...
Research Article

2. Integrable Boundary Conditions for the Hirota-Miwa Equation and Lie Algebras

Ismagil Habibullin, Aigul Khakimova
Pages: 393 - 413
Systems of discrete equations on a quadrilateral graph related to the series DN(2) of the affine Lie algebras are studied. The systems are derived from the Hirota-Miwa equation by imposing boundary conditions compatible with the integrability property. The Lax pairs for the systems are presented. It...
Research Article

3. On the global dynamics of a three-dimensional forced-damped differential system

Jaume Llibre, Y. Paulina Martínez, Claudia Valls
Pages: 414 - 428
In this paper by using the Poincaré compactification of ℝ3 we make a global analysis of the model x′ = −ax + y + yz, y′ = x − ay + bxz, z′ = cz − bxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values...
Research Article

4. Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions

John Cobb, Alex Kasman, Albert Serna, Monique Sparkman
Pages: 429 - 452
Quaternion-valued solutions to the non-commutative KdV equation are produced using determinants. The solutions produced in this way are (breather) soliton solutions, rational solutions, spatially periodic solutions and hybrids of these three basic types. A complete characterization of the parameters...
Research Article

5. Hierarchies of q-discrete Painlevé equations

Huda Alrashdi, Nalini Joshi, Dinh Thi Tran
Pages: 453 - 477
In this paper, we construct a new hierarchy based on the third q-discrete Painlevé equation (qPIII) and also study the hierarchy of the second q-discrete Painlevé equation (qPII). Both hierarchies are derived by using reductions of the general lattice modified Korteweg-de Vries equation. Our results...
Research Article

6. Nonautonomous symmetries of the KdV equation and step-like solutions

V.E. Adler
Pages: 478 - 493
We study solutions of the KdV equation governed by a stationary equation for symmetries from the non-commutative subalgebra, namely, for a linear combination of the master-symmetry and the scaling symmetry. The constraint under study is equivalent to a sixth order nonautonomous ODE possessing two first...
Research Article

7. Group analysis of the generalized Burnett equations

Alexander V. Bobylev, Sergey V. Meleshko
Pages: 494 - 508
In this paper group properties of the so-called Generalized Burnett equations are studied. In contrast to the classical Burnett equations these equations are well-posed and therefore can be used in applications. We consider the one-dimensional version of the generalized Burnett equations for Maxwell...
Research Article

8. Global dynamics of a Lotka–Volterra system in ℝ3

Jaume Llibre, Y. Paulina Martínez, Claudia Valls
Pages: 509 - 519
In this work we consider the Lotka–Volterra system in ℝ3 x˙=−x(x−y−z),      y˙=−y(−x+y−z),       z˙=−z(−x−y+z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they...