The paper presents the design of nonlinear state feedback controller for a rigid manipulator. In order to obtain such controllers, a partial differential equation, HJB equation, should be solved, which is difficult to find a closed solution of that. In this paper, an efficient method using Taylor series expansion of nonlinear terms is used to tackle this problem. The tracking performance of the...

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h → 0 is either the nonlinear von Kármán plate equation or the linear fourth order Germain-Lagrange equa...

This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of the HJB equation. Furthermore, via this explicit viscosity solution, we obta...

1. Introduction The stationary behaviour of semiconductor devices is governed by a set of nonlinear elliptic partial differential equations. This includes a nonlinear Poisson equation and two nonlinear continuity equations. Using Gummel's method [2] we can decouple the nonlinear elliptic system so that at each step we solve an equation of the form

A generalized inverse scattering method has been developed for arbitrary n dimensional Lax equations. Subsequently, the method has been used to obtain N soliton solutions of a vector higher order nonlinear Schrödinger equation, proposed by us. It has been shown that under suitable reduction, vector higher order nonlinear Schrödinger equation reduces to higher order nonlinear Schrödinger equatio...

In the age of technology, it is vital to cool down different parts of a device to use it more beneficially. Using nanofluids is one of the most common methods which has shown very effective results. In this paper, we have rephrased a classic equation in fluid mechanics, i.e. the Falkner-Skan boundary layer equation, in order to be used for nanofluid. This nonlinear equation, which was presented...

Articles you may be interested in Multi-peak solution for nonlinear magnetic Choquard type equation Smooth soliton solutions of a new integrable equation by Qiao Optimal solution for the viscous nonlinear dispersive wave equation We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential. C 2012 American Institute of Physics.

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

The KP equation, which is an integrable nonlinear evolution equation in 2 + 1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the...

Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3?1)-dimensional modified KdV–Zakharov– Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equ...