Journal of Nonlinear Mathematical Physics

In this paper we identify certain peculiar systems of 2 discrete-time evolution equations, x˜n=F(n)(x1,x2),   n=1,2, which are algebraically solvable. Here ℓ is the “discrete-time” independent variable taking integer values (ℓ = 0, 1, 2,...), xn ≡ xn(ℓ) are 2 dependent variables, and x˜n≡xn(ℓ+1) are...

The ‘restoration method’ is a novel method we recently introduced for systematically deriving discrete Painlevé equations. In this method we start from a given Painlevé equation, typically with E8(1) symmetry, obtain its autonomous limit and construct all possible QRT-canonical forms of mappings that...

We consider slant normal magnetic curves in (2n + 1)-dimensional S-manifolds. We prove that γ is a slant normal magnetic curve in an S-manifold (M2m+s, φ, ξα, ηα, g) if and only if it belongs to a list of slant φ-curves satisfying some special curvature equations. This list consists of some specific...

We study the simple-looking scalar integrable equation fxxt − 3(fx ft − 1) = 0, which is related (in different ways) to the Novikov, Hirota-Satsuma and Sawada-Kotera equations. For this equation we present a Lax pair, a Bäcklund transformation, soliton and merging soliton solutions (some exhibiting instabilities),...

In this paper by using the Poincaré compactification in ℝ3 we make a global analysis of the model x′ = z, y′ = b(x−dy), z′ = x(x2 −1)+y+cz with b ∈ ℝ and c, d ∈ ℝ+, here known as the three-dimensional Newell–Whitehead system. We give the complete description of its dynamics on the sphere at infinity....

In this paper, a modification of the standard geophysical equatorial β-plane model equations, incorporating a gravitational-correction term in the tangent plane approximation, is derived. We present an exact solution to meet the modified governing equations, whose form is explicit in the Lagrangian framework...

For a scalar evolution equation ut = K(t, x, u, ux, ..., u2m+1) with m ≥ 1, the cohomology space H1,2(ℛ∞) is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for ut = K for which the equation is Hamiltonian is also shown...

In this article we develop a generalization of the Hamilton-Jacobi theory, by considering in the cotangent bundle an involutive system of dynamical equations.