Journal of Nonlinear Mathematical Physics

We examine an aspect of the modelling of the underlying fluid motion in the equatorial region of the ocean. In particular, we assess whether nonlinearity is inherently vital in capturing the three-dimensional upwelling and downwelling phenomena. A recent applied mathematical approach has successfully...

In this paper, we deal with contractions of Lie algebras. We use two invariant functions of Lie algebras as a tool, named ψ and φ function, respectively, which have a great application in Physics due to their remarkable properties. We focus the study of these functions in the frame of the filiform Lie...

In this paper, we construct a Darboux transformation and the related Bäcklund transformation for the super-symmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is also worked out. We demonstrate that these are natural extensions of the similar results of the Sawada-Kotera...

In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous...

The results of inverse scattering problem associated with the initial-boundary value problem (IBVP) for the Korteweg–de Vries (KdV) equation with dominant surface tension are formulated. The necessary and sufficient conditions for given functions to be the left- and right-reflection coefficients of the...

We use previous results concerning the time evolution of the zeros xn(t) of time-dependent polynomials pN(z; t) or entire functions F(z; t) of the complex variable z, in order to identify lots of nonlinearly-coupled, finite or infinite, systems of Ordinary Differential Equations the solutions of which...

This paper is a continuation of our previous work in which we studied a sl(3, ℂ) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the corresponding integrable hierarchy of nonlinear evolution equations. Now, we shall demonstrate how one can construct special solutions...

We consider the anti-de Sitter space 𝔿13 and the hyperbolic Hopf fibration h:𝔿13(1)→𝔿2(1/2). Using their description in terms of paraquaternions, we study the magnetic curves of the hyperbolic Hopf vector field. A complete classification is obtained for light-like magnetic curves, showing in particular...

Symplectic reflection algebra H1,η(G) has a T(G)-dimensional space of traces whereas, when considered as a superalgebra with a natural parity, it has an S(G)-dimensional space of supertraces. The values of T(G) and S(G) depend on the symplectic reflection group G and do not depend on the parameter η. In...

We exhibit some families of Riccati differential equations in the complex domain having elliptic coefficients and study the problem of understanding the cases where there are no multivalued solutions. We give criteria ensuring that all the solutions to these equations are meromorphic functions defined...