Volume 27, Issue 4, September 2020

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...

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...

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...

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...

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...

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.

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...

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...

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.

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.

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,...

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).