Journal of Nonlinear Mathematical Physics

In this note we give the conditions for the existence of algebraic geodesics on some two-dimensional quadrics, namely, on hyperbolic paraboloids and elliptic paraboloids. It appears that in some cases, such geodesics are the rational space curves.

A previously unknown bright N-soliton solution for an intermediate nonlinear Schrödinger equation of focusing type is presented. This equation is constructed as a reduction of an integrable system related to a Sato equation of a 2-component KP hierarchy for certain differential-difference dispersion...

Using a concept of strong necessary conditions we derive the Bogomolny decomposition for systems of two generalized elliptic and parabolic nonlinear partial differential equations (NPDE) of the second order. The generalization means that the equation coefficients depend on the field variables. According...

We study Gaussian beams for the wave equation on a Riemannian manifold. For the transport equation we geometrize the leading term at the center of the Gaussian beam. More precisely, if u(x,t)=eiPθ(x,t)(u0(x,t)+u1(x,t)iP+u2(x,t)(iP)2+⋯) is a Gaussian beam propagating along a geodesic c, then we show...

This paper presents a new third-order trajectory solution in Lagrangian form for the water particles in a wave-current interaction flow based on an Euler–Lagrange transformation. The explicit parametric solution highlights the trajectory of a water particle and the wave kinematics above the mean water...

Starting from any representation of the Lie algebra ℊ on the finite dimensional vector space V we can construct the representation on the space Aut(V ). These representations are of the type of ad. That is one of the reasons, why it is important to study the adjoint representation of the Lie algebra...

Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using...

Nicodemi and Prisco recently proposed a model for X-chromosome inactivation in mammals, explaining this phenomenon in terms of a spontaneous symmetry-breaking mechanism [Phys. Rev. Lett. 99 (2007) 108104]. Here we provide a mean-field version of their model.

We identify a solvable dynamical system — interpretable to some extent as a many-body problem — and point out that — for an appropriate assignment of its parameters — it is entirely isochronous, namely all its nonsingular solutions are completely periodic (i.e., periodic in all degrees of freedom) with...