Problems Of Nonlinear Theory Research Articles

Exploration of New Solitons for the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model

The key objective of the current manuscript was to investigate the exact solutions of the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. For this purpose, we applied two reliable and efficient approaches; specifically, the modified simple equation (MSE) and exponential rational function (ERF) techniques. The methods considered in this paper offer solutions for problems in nonlinear theory and mathematical physics practice. We also present solutions obtained graphically with the Maple package program.

COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spaces cannot be uniformly embedded into a reflexive space. We give a necessary condition for a metric space to be coarsely or uniformly embeddable in a uniformly convex space.

The Bubnov–Galerkin Method for the Approximate Solution of Boundary Value Problems of Nonlinear Theory of Thin Shells

The Bubnov–Galerkin Method for the Approximate Solution of Boundary Value Problems of Nonlinear Theory of Thin Shells

Boundary elements and nonclassical differences in the problems of nonlinear theory of elasticity

We propose a method of simultaneous application of the fundamental solution of the Lame equations, boundary elements, nonclassical finite-difference relations, and the procedure of continuation of solutions in a parameter to the solutions two-dimensional problems for physically nonlinear inhomogeneous media.

Problems of non-linear theory in differential scanning calorimetry

The problems of DSC non-linear theory, connected with the dependence of the thermophysical parameters upon the temperature, are discussed. The changes in thle form of the thermal energy curve recorded by the device as results of the thermaconductivity jump and heat capacity shift taken into account in the course of transformation are shown. A correct non-linear DSC model is formulated. The mather matical apparatus and some simplifying notions for calculation with the non-lineamodel are suggested. The interpretation of a calorimetric curve of an adiabatic scan. ning microcalorimeter over a pretransition range of temperatures is given as an example

On a boundary value problem in nonlinear theory of thin elastic plates

In this paper boundary value problems for the system of nonlinear partial differential equations for displacement, governing the equilibrium state of thin elastic plates, are solved. The abstract calculus of variarions is used.

On Finite Symmetrical Deflections of Thin Shells of Revolution

Recent simplifications of linear shell theory through consideration of transverse shear deformations and stress moments with axes normal to the shell middle surface suggest analogous approaches to the corresponding problem of nonlinear theory. As a first step in this direction consideration is given here to the classical subject of finite symmetrical deformations of shells of revolution. The principal new results of the present analysis concern the form of strain-displacement and compatibility differential equations.

On the finite deformation of a sector plate

In this paper an investigation is given into the behaviour of the stress singularity which occurs in the linear theory of elasticity at the deformation of a sector plate, if finite deformations are considered. It is assumed that for very small deformations Hooke's law is valid, and only in the neighbourhood of the singularity Hooke's law has to be extended. This extension is not unique. It is shown that for two different strain-energy functions, which have the same asymptotic expansion for infinitesimal deformations, the behaviour of the solutions is quite different. One of the strain-energy functions leads to a bounded solution, while the solution, obtained from the other one becomes singular for the case of contraction. As it cannot be expected that it will be possible to decide on an experimental basis about the right extension, an assertion about the difference in smoothness of solutions to problems in linear and non-linear theory cannot be given. An open question is raised: whether or not the requirement of regularity for this kind of problems in non-linear theory can be posed as a restriction on the admissible energy functions.