Painlevé analysis and similarity reductions for the magma equation.
Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation
Periodic and solitary wave solutions of two component Zakharov-Yajima-Oikawa system, using Madelung's approach.
Periodic traveling waves in the system of linearly coupled nonlinear oscillators on 2D-lattice
In this paper we obtain results on existence of non-constant periodic traveling waves with arbitrary speed in infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. Sufficient conditions for the existence of such solutions are obtained with the aid of critical point method and linking theorem.
Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method.
Perron-Frobenius operators and the Klein-Gordon equation
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...
Perturbation of a solitary wave of the nonlinear Klein-Gordon equation.
Perturbations of Systems Describing the Motion of a Particle in Central Fields
The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.
Perturbations of the harmonic map equation
We consider perturbations of the harmonic map equation in the case where the source and target manifolds are closed riemannian manifolds and the latter is in addition of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. For generic perturbations the set of solutions is finite and we present a count of this set. An important ingredient for our analysis is...
Phase transition in dynamical systems: defining classes of universality for two-dimensional Hamiltonian mappings via critical exponents.
Poisson-Nijenhuis structures
Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group.
Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds
In this paper we describe moving frames and differential invariants for curves in two different -graded parabolic manifolds , and , and we define differential invariants of projective-type. We then show that, in the first case, there are geometric flows in inducing equations of KdV-type in the projective-type differential invariants when proper initial conditions are chosen. We also show that geometric Poisson brackets in the space of differential invariants of curves in can be reduced...
Prolongation loop algebras for a solitonic system of equations.
Proof of the Treves theorem on the KdV hierarchy
A new, shorter, proof of the Treves theorem on an algebraic criterion for the first integrals of the KdV hierarchy is given, along with an addition to the theorem.
Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation
In this paper, we study the linear Schrödinger equation over the d-dimensional torus, with small values of the perturbing potential. We consider numerical approximations of the associated solutions obtained by a symplectic splitting method (to discretize the time variable) in combination with the Fast Fourier Transform algorithm (to discretize the space variable). In this fully discrete setting, we prove that the regularity of the initial datum is preserved over long times, i.e. times that are...
Prym-Tjurin varieties and the Hitchin map.