Journal of Nonlinear Mathematical Physics

In this work we consider the modified Michaelis-Menten equation in biochemistry x˙=-a(E-y)x+by,  y˙=a(E-y)x-(b+r)y,  z˙=ry. It models the enzyme kinetics. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability...

In Ergodic Theory it is natural to consider the pointwise convergence of finite time averages of functions with respect to the flow of dynamical systems. Since the pointwise convergence is too weak for applications to Hamiltonian Perturbation Theory, requiring differentiability, we first introduce regularized...

We study the nonlinear self-adjointness of a class of quasilinear 2D second order evolution equations by applying the method of Ibragimov. Which enables one to establish the conservation laws for any differential equation. We first obtain conditions determining the self-adjointness for a sub-class in...

The nonclassical symmetries method is applied to a class of reaction-diffusion equations with nonlinear source, i.e. ut=uxx+cux+R(u, x). Several cases are obtained by using suitable solutions of the heir-equations as described in [M.C. Nucci, Nonclassical symmetries as special solutions of heir-equations,...

A hierarchy of new nonlinear evolution equations is proposed, which are composed of the positive and negative coupled KdV flows. Based on the theory of algebraic curve, the corresponding flows are straightened under the Abel-Jacobi coordinates. The meromorphic function ϕ, the Baker-Akhiezer vector ψ¯ ,...

In this paper we develop a straightforward procedure to construct higher dimensional isochronous Hamiltonian systems. We first show that a class of singular Hamiltonian systems obtained through the Ω-modified procedure is equivalent to constrained Newtonian systems. Even though such systems admit isochronous...

The (2+1)-dimensional Davey-Stewartson-like equations with variable coefficients have the applications in the ultra-relativistic degenerate dense plasmas and Bose-Einstein condensates. Via the Bell polynomials and symbolic computation, the bilinear form, Bäcklund transformation and Lax pair for such...

We study the integrable discretization of the coupled integrable dispersionless equations. Two semi-discrete version and one full-discrete version of the system are given via Hirota's bilinear method. Soliton solutions for the derived discrete systems are also presented.

A recently proposed three-component Camassa-Holm equation is considered. It is shown that this system is a bi-Hamiltonian system.

Boundary value problems for integrable nonlinear evolution PDEs, like the modified KdV equation, formulated on the half-line can be analyzed by the so-called unified transform method. For the modified KdV equation, this method yields the solution in terms of the solution of a matrix Riemann-Hilbert problem...

Recently a solvable N-body problem featuring several free parameters has been investigated, and conditions on these parameters have been identified which guarantee that this system is isochronous (all its solutions are periodic with a fixed period) and that it possesses equilibria. The N coordinates...