Exact Heisenberg operator solutions for independent ‘sinusoidal coordinates’ as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multi-parti...

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operatorvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the larg...

In this paper, an optimM trajectory planning problem for a single-link t_exiblejoint manipulator is studied. A global feedback-linearization technique is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formu/a for the optimal solution of the problem is derived and the solution is shown to be unique. I...

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...

Exact or approximate solutions to constrained linear model predictive control (MPC) problems can be precomputed off-line in an explicit form as a piecewise linear state feedback defined on a polyhedral partition of the state space. However, the complexity of the polyhedral partition often increases rapidly with the dimension of the state vector, and the number of constraints. Recently, several ...

in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

In this paper, we establish exact solutions for nonlinear evolution equations. The homogeneous balance method is used to construct exact travelling wave solutions of the CalogeroDegasperis (CD) and Potential Kadomstev-Petviashvili (PKP) equations, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many new f...

As a numerical method for solving ordinary differential equations y′ = f(x, y), the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for f(x, y) to a finite system that is sufficient and necessary for the improved ...

Exact numerical schemes have previously been obtained for some linear retarded delay differential equations and systems. Those were derived from explicit expressions of the exact solutions, expressed in form perturbed difference systems, involving values at previous intervals. In this work, we propose to directly obtain same type fundamental solutions equations, by considering vector with compo...