Journal of Nonlinear Mathematical Physics

Volume 24, Issue 4, September 2017
Letter to Editor

1. Bäcklund transformations between four Lax-integrable 3D equations

Oleg I. Morozov, Maxim V. Pavlov
Pages: 465 - 468
Recently a classification of contactly-nonequivalent three-dimensional linearly degenerate equations of the second order was presented by E.V. Ferapontov and J. Moss. The equations are Lax-integrable. In our paper we prove that all these equations are connected with each other by appropriate Bäcklund...
Letter to Editor

2. Novel differential algorithm to evaluate all the zeros of any generic polynomial

Francesco Calogero
Pages: 469 - 472
A novel, remarkably neat, differential algorithm is introduced, which is suitable to evaluate all the zeros of a generic polynomial of arbitrary degree N.
Research Article

3. On the Darboux integrability of a three–dimensional forced–damped differential system

Jaume Llibre, Regilene Oliveira, Claudia Valls
Pages: 473 - 494
In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. In this paper we study the opposite to its chaotic motion, i.e. its integrability,...
Research Article

4. New Properties of the Zeros of Krall Polynomials

Oksana Bihun
Pages: 495 - 515
We identify a new class of algebraic relations satisfied by the zeros of orthogonal polynomials that are eigenfunctions of linear differential operators of order higher than two, known as Krall polynomials. Given an orthogonal polynomial family {pv(x)}v=0∞ , we relate the zeros of the polynomial...
Research Article

5. Lie symmetry analysis, conservation laws and analytical solutions of a time-fractional generalized KdV-type equation*

Xiu-Bin Wang, Shou-Fu Tian, Chun-Yan Qin, Tian-Tian Zhang
Pages: 516 - 530
Under investigation in this work is the time-fractional generalized KdV-type equation, which occurs in different contexts in mathematical physics. Lie group analysis method is presented to explicitly study its vector fields and symmetry reductions. Furthermore, two straightforward methods are employed...
Research Article

6. Generalized Conditional Symmetries, Related Solutions and Conservation Laws of the Grad-Shafranov Equation with Arbitrary Flow

Rodica Cimpoiasu
Pages: 531 - 544
The generalized conditional symmetry (GCS) method is applied to the case of a generalized Grad-Shafranov equation (GGSE) with incompressible flow of arbitrary direction. We investigate the conditions which yield the GGSE that admits a special class of second-order GCSs. Three GCS generators and the associated...
Research Article

7. The peculiar (monic) polynomials, the zeros of which equal their coefficients

F. Calogero, F. Leyvraz
Pages: 545 - 555
We evaluate the number of complex monic polynomials, of arbitrary degree N, the zeros of which are equal to their coefficients. In the following, we call polynomials with this property peculiar polynomials. We further show that the problem of determining the peculiar polynomials of degree N simplifies...
Research Article

8. Einstein-like Lorentzian Lie groups of dimension four

Amirhesam Zaeim
Pages: 556 - 570
Einstein-like examples of four-dimensional Lorentzian Lie groups are listed and geometric properties of each class have been investigated.
Research Article

9. Note on algebro-geometric solutions to triangular Schlesinger systems

Vladimir Dragović, Vasilisa Shramchenko
Pages: 571 - 583
We construct algebro-geometric upper triangular solutions of rank two Schlesinger systems. Using these solutions we derive two families of solutions to the sixth Painlevé equation with parameters (1/8, ‒1/8, 1/8, 3=8) expressed in simple forms using periods of differentials on elliptic curves. Similarly...
Research Article

10. Liouville Integrability of Conservative Peakons for a Modified CH equation

Xiangke Chang, Jacek Szmigielski
Pages: 584 - 595
The modified Camassa-Holm (also called FORQ) equation is one of numerous cousins of the Camassa-Holm equation possessing non-smoth solitons (peakons) as special solutions. The peakon sector of solutions is not uniquely defined: in one peakon sector (dissipativea) the Sobolev H1 norm is not preserved,...
Research Article

11. Holomorphic last multipliers on complex manifolds

Mircea Crasmareanu, Cristian Ida, Paul Popescu
Pages: 596 - 619
The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an associated real ODE system and we are interested how we can relate...
Research Article

12. The modified Korteweg-de Vries equation on the quarter plane with t-periodic data

Guenbo Hwang
Pages: 620 - 634
We study the modified Korteweg-de Vries equation posed on the quarter plane with asymptotically t-periodic Dirichlet boundary datum u(0,t) in the sense that u(0,t) tends to a periodic function g̃0 (t) with period τ as t → ∞. We consider the perturbative expansion of the solution in a small ε > 0....