Related papers: A General Exact Closed-Form Solution for Nonlinear…
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…
The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical…
We study the existence and multiplicity of solutions and the global solution curve of the following free boundary value problem, arising in plasma physics, see R. Temam [18], and H. Berestycki and H. Brezis [3]: find a function $u(x)$ and a…
The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$…
We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear planar double pendulum perturbed by smooth or non--smooth functions.
A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilton equations of motion describing nonlinear betatron…
This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
We investigate the behavior of rotating incompressible flows near a non-flat horizontal bottom. In the flat case, the velocity profile is given explicitly by a simple linear ODE. When bottom variations are taken into account, it is governed…
In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…