A nonlinear perturbation ofd 2 u/dx 2+λu,u(−∞)=u+∞)=0

1988 ◽  
Vol 152 (1) ◽  
pp. 159-169
Author(s):  
R. Ortega
Keyword(s):  
Nonlinear Perturbation

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

On a convergent nonlinear perturbation theory without small denominators or secular terms

1976 ◽  
Vol 17 (1) ◽  
pp. 121-140 ◽  
Author(s):  
Charles R. Eminhizer ◽  
Robert H. G. Helleman ◽  
Elliott W. Montroll
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Perturbation ◽  
Small Denominators ◽  
Secular Terms

A Study on the Instability of Disk-Shaped Gear

1999 ◽  
Author(s):  
Guangming Ren ◽  
Litang Yan
Keyword(s):  
Perturbation Method ◽  
Traveling Wave ◽  
Vibration Characteristics ◽  
Exciting Force ◽  
Nonlinear Perturbation ◽  
The Self ◽  
Experimental Investigations ◽  
Damping Force ◽  
Bevel Gears ◽  
Theory And Experiment

Abstract In this paper the theory and experiment concerning vibration instability of disk-shaped gear are presented. At first the self-exciting force of gear is searched and the works done by the exciting force and damping force are analyzed. Then the vibration instability of the disk-shaped plain gear is studied with multiple scale’s method of the nonlinear perturbation method. The vibration characteristics of a coupled pair of bevel gears are investigated experimentally. Both theoretical and experimental investigations show that there are actually self-exciting vibrations on the gear. Under certain conditions the forward traveling wave vibration of the driving gear and the backward traveling wave vibration of the driven gear can be instable.

scholarly journals A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 82 ◽  
Author(s):  
Watcharin Chartbupapan ◽  
Ovidiu Bagdasar ◽  
Kanit Mukdasai
Keyword(s):  
Asymptotic Stability ◽  
Stability Criterion ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Neutral System ◽  
The Novel ◽  
Neutral Systems ◽  
Fractional Differential ◽  
Delay Dependent ◽  
Single Constant

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.

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