Journal of Nonlinear Mathematical Physics

Volume 27, Issue 4, September 2020
Letter to Editor

1. On the hierarchies of the fully nonlinear Möbius-invariant and symmetry-integrable evolution equations of order three

Marianna Euler, Norbert Euler
Pages: 521 - 528
This is a follow-up paper to the results published in Studies in Applied Mathematics 143, 139–156 (2019), where we reported a classification of 3rd- and 5th-order semi-linear symmetry-integrable evolution equations that are invariant under the Möbius transformation, which includes a list of fully nonlinear...
Research Article

2. Minimal surfaces associated with orthogonal polynomials

Vincent Chalifour, Alfred Michel Grundland
Pages: 529 - 549
This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces approach defined by the Enneper-Weierstrass formula for immersion and...
Research Article

3. Study on geometric structures on Lie algebroids with optimal control applications

Esmaeil Peyghan, Liviu Popescu
Pages: 550 - 580
We construct ρ£-covariant derivatives in π*π as the generalization of covariant derivative in π*π to £πE. Moreover, we introduce Berwald and Yano derivatives as two important classes of ρ£-covariant derivatives in π*π and we study properties of them. Finally, we solve an optimal control problem using...
Research Article

4. Nonlocal symmetries and group invariant solutions for the coupled variable-coefficient Newell-Whitehead system

Yarong Xia, Ruoxia Yao, Xiangpeng Xin
Pages: 581 - 591
Starting from the Lax pairs, the nonlocal symmetries of the coupled variable-coefficient Newell-Whitehead system are obtained. By introducing an appropriate auxiliary dependent variable, the nonlocal symmetries are localized to Lie point symmetries and the coupled variable-coefficient Newell-Whitehead...
Research Article

5. Asymptotics behavior for the integrable nonlinear Schrödinger equation with quartic terms: Cauchy problem

Lin Huang
Pages: 592 - 615
We consider the Cauchy problem of integrable nonlinear Schrödinger equation with quartic terms on the line. The first part of the paper considers the Riemann-Hilbert formula via the unified method(also known as the Fokas method). The second part of the paper establishes asymptotic formulas for the solution...
Research Article

6. On the discretization of Darboux Integrable Systems

Kostyantyn Zheltukhin, Natalya Zheltukhina
Pages: 616 - 632
We study the discretization of Darboux integrable systems. The discretization is done using x-, y-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
Research Article

7. Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation

Xiaoxue Xu, Cewen Cao, Guangyao Zhang
Pages: 633 - 646
Based on integrable Hamiltonian systems related to the derivative Schwarzian Korteweg-de Vries (SKdV) equation, a novel discrete Lax pair for the lattice SKdV (lSKdV) equation is given by two copies of a Darboux transformation which can be used to derive an integrable symplectic correspondence. Resorting...
Research Article

8. Decomposition of 2-Soliton Solutions for the Good Boussinesq Equations

Vesselin Vatchev
Pages: 647 - 663
We consider decompositions of two-soliton solutions for the good Boussinesq equation obtained by the Hirota method and the Wronskian technique. The explicit forms of the components are used to study the dynamics of 2-soliton solutions. An interpretation in the context of eigenvalue problems arising from...
Research Article

9. Integrability conditions of a weak saddle in generalized Liénard-like complex polynomial differential systems

Jaume Giné, Claudia Valls
Pages: 664 - 678
We consider the complex differential system x˙=x+yf(x),   y˙=−y+xf(y), where f is the analytic function f(z)=∑j=1∞ajzj with aj ∈ ℂ. This system has a weak saddle at the origin and is a generalization of complex Liénard systems. In this work we study its local analytic integrability.
Research Article

10. Symmetry classification of scalar Ito equations with multiplicative noise

Giuseppe Gaeta, Francesco Spadaro
Pages: 679 - 687
We provide a symmetry classification of scalar stochastic equations with multiplicative noise. These equations can be integrated by means of the Kozlov procedure, by passing to symmetry adapted variables.
Research Article

11. Gambier lattices and other linearisable systems

Basil Grammaticos, Alfred Ramani
Pages: 688 - 696
We propose two different appraoches to extending the Gambier mapping to a two-dimensional lattice equation. A first approach relies on a hypothesis of separate evolutions in each of the two directions. We show that known equations like the Startsev-Garifullin-Yamilov equation, the Hietarinta equation,...
Research Article

12. Trigonal Toda Lattice Equation

Shigeki Matsutani
Pages: 697 - 704
In this article, we give the trigonal Toda lattice equation, −12d3dt3qℓ(t)=eqℓ+1(t)+eqℓ+ζ3(t)++eqℓ+ζ32(t)−3eqℓ(t), for a lattice point ℓ ∈ 𝕑[ζ3] as a directed 6-regular graph where ζ3=e2π−1/3, and its elliptic solution for the curve y(y − s) = x 3, (s ≠ 0).