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This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
This paper aims to find new explicit solutions including multi-soliton, multi-positon, multi-negaton, and multi-periodic for a coupled Volterra lattice system which is an integrable discrete version of the coupled KdV equation. The…
There exists a remarkable connection between the quantum mechanical Landau-Zener problem and purely classical-mechanical problem of a ball rolling on a Cornu spiral. This correspondence allows us to calculate a complicated multiple…
In this note we obtain the solutions of four $q$-functional equations and express the solutions in $q$-operator forms. These equations give sufficient conditions for $q$-operator methods.
We establish the multiplicity of positive solutions to a quasilinear Neumann problem in expanding balls and hemispheres with critical exponent in the boundary condition.
For the $n$-body problem in spaces of negative constant Gaussian curvature, we prove for a class of negative hyperbolic rotopulsators that if that class exists, the configurations of the point masses of these rotopulsators have to be…
The rotated multipliers method is performed in the case of the boundary stabilization by means of a(linear or non-linear) Neumann feedback. this method leads to new geometrical cases concerning the "active" part of the boundary where the…
We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…
In this paper, we present rotational and self-similar solutions for the compressible Euler equations in R^3 using the separation method. These solutions partly complement Yuen's irrotational and elliptic solutions in R^3 [Commun. Nonlinear…
The field equations of $f(R)$ gravity are rewritten in the form of obvious wave equations with the stress-energy pseudotensor of the matter fields and the gravitational field as its source under the de Donder condition. The method of…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
Starting from a Pfaffian equation in dimension $N$ and focusing on compact solutions for it, we place in perspective the variational method used in [29] to solve Hilbert's 16th problem. In addition to exploring how this viewpoint can help…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
In this article we study mild solutions for the forced, incompressible fractional Navier-Stokes equations. These solutions are classically obtained via a fixed-point argument which relies on suitable estimates for the initial data, the…
We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs an integrable forced version of this equation. The forcing consists of terms involving quadratic products of…
In this article, we construct matrices associated to Pachner $\frac{n-1}{2}$-$\frac{n-1}{2}$ moves for odd $n$ and matrices associated to Pachner $(\frac{n}{2}-1)$-$\frac{n}{2}$ moves for even $n$. The entries of these matrices are rational…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…
Power Series Solution method has been used traditionally for to solve Linear Differential Equations, in Ordinary and Partial form. But this method has been limited to this kind of problems. We present the solution of problems of Non Linear…