Journal of Nonlinear Mathematical Physics

Volume 28, Issue 1, March 2021
Research Article

1. Nurowski’s Conformal Class of a Maximally Symmetric (2,3,5)-Distribution and its Ricci-flat Representatives

Matthew Randall
Pages: 1 - 13
We show that the solutions to the second-order differential equation associated to the generalised Chazy equation with parameters k = 2 and k = 3 naturally show up in the conformal rescaling that takes a representative metric in Nurowski’s conformal class associated to a maximally symmetric (2,3,5)-distribution...
Research Article

2. On the Coupled Dispersionless-type Equations and the Short Pulse-type Equations

Juan Hu, Jia-Liang Ji, Guo-Fu Yu
Pages: 14 - 26
In this paper, we study the correspondence between the Coupled Dispersionless (CD)-type equations and the Short Pulse (SP)-type equations. From the real and complex modified CD equations, we construct the real and complex Modified Short Pulse (mSP) equations geometrically and algebraically. From the...
Research Article

3. The (N + 1)-Dimensional Burgers Equation: A Bilinear Extension, Vortex, Fusion and Rational Solutions

Hongli An, Engui Fan, Manwai Yuen
Pages: 27 - 37
In this paper, by introducing a fractional transformation, we obtain a bilinear formulation for the (N + 1)-dimensional Burgers equation. Such a formulation constitutes a bilinear extension to the (N + 1)-dimensional Cole-Hopf transformation between the (N + 1)-dimensional Burgers system and generalized...
Research Article

4. Inverse Scattering Transformation for the Fokas–Lenells Equation with Nonzero Boundary Conditions

Yi Zhao, Engui Fan
Pages: 38 - 52
In this article, we focus on the inverse scattering transformation for the Fokas–Lenells (FL) equation with nonzero boundary conditions via the Riemann–Hilbert (RH) approach. Based on the Lax pair of the FL equation, the analyticity, symmetry and asymptotic behavior of the Jost solutions and scattering...
Research Article

5. The Miura Links of the Symmetries in the q-Deformed Case

Siqi Jian, Jipeng Cheng
Pages: 53 - 67
In this paper, we first construct the squared eigenfunction symmetries for the q-deformed Kadomtsev–Petviashvili (KP) and q-deformed modified KP hierarchies, including the unconstrained and constrained cases. Then the Miura links of the squared eigenfunction symmetries are investigated. At last, we also...
Research Article

6. Focusing NLS Equations with Nonzero Boundary Conditions: Triangular Representations and Direct Scattering

Cornelis van der Mee
Pages: 68 - 89
In this article we derive the triangular representations of the fundamental eigensolutions of the focusing 1 + 1 AKNS system with symmetric nonvanishing boundary conditions. Its continuous spectrum equals 𝕉∪[-iμ,iμ] , where μ is the absolute value of the AKNS solution at spatial infinity. We...
Research Article

7. Symmetries, Conservation Laws, Invariant Solutions and Difference Schemes of the One-dimensional Green-Naghdi Equations

V.A. Dorodnitsyn, E.I. Kaptsov, S.V. Meleshko
Pages: 90 - 107
The paper is devoted to the Lie group properties of the one-dimensional Green-Naghdi equations describing the behavior of fluid flow over uneven bottom topography. The bottom topography is incorporated into the Green-Naghdi equations in two ways: in the classical Green-Naghdi form and in the approximated...
Research Article

8. On Hermitian and Skew-Hermitian Matrix Algebras over Octonions

Arezoo Zohrabi, Pasha Zusmanovich
Pages: 108 - 122
We prove simplicity of algebras in the title, and compute their δ-derivations and symmetric associative forms.
Research Article

9. Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H1,V(I2(2m + 1)) II

I.A. Batalin, S.E. Konstein, I.V. Tyutin
Pages: 123 - 133
The algebra 𝒣≔H1,ν(I2(2m+1)) of observables of the Calogero model based on the root system I2(2m + 1) has an m-dimensional space of traces and an (m + 1)-dimensional space of supertraces. In the preceding paper we found all values of the parameter ν for which either the space of traces contains...
Research Article

10. The Complex Hamiltonian Systems and Quasi-periodic Solutions in the Hirota Equation

Jinbing Chen, Rong Tong
Pages: 134 - 149
The Hirota equation is reduced to a pair of complex Finite-dimensional Hamiltonian Systems (FDHSs) with real-valued Hamiltonians, which are proven to be completely integrable in the Liouville sense. It turns out that involutive solutions of the complex FDHSs yield finite parametric solutions of the Hirota...
Research Article

11. Exact Solutions of the Nonlinear Fin Problem with Temperature-dependent Coefficients

Özlem Orhan, Teoman Özer
Pages: 150 - 170
The analytical solutions of a nonlinear fin problem with variable thermal conductivity and heat transfer coefficients are investigated by considering theory of Lie groups and its relations with λ-symmetries and Prelle-Singer procedure. Additionally, the classification problem with respect to different...