Constructing explicit homoclinic solution of oscillators: An improvement for perturbation procedure based on nonlinear time transformation

2017 ◽  
Vol 48 ◽  
pp. 123-139 ◽  
Author(s):  
Y.Y. Chen ◽  
S.H. Chen ◽  
W. Zhao
Keyword(s):  
Homoclinic Solution ◽  
Time Transformation ◽  
Perturbation Procedure ◽  
Nonlinear Time Transformation

Evidence for the Nonintegrability of a Water Wave Equation in 2+1 Dimensions

2004 ◽  
Vol 59 (10) ◽  
pp. 640-644 ◽  
Author(s):  
P. R. Gordoa ◽  
A. Pickering ◽  
M. Senthilvelan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Water Waves ◽  
Water Wave ◽  
Classification Scheme ◽  
Time Transformation ◽  
Series Solutions ◽  
Holm Equation ◽  
Proposed Model ◽  
Nonlinear Time Transformation

We provide evidence of the nonintegrability of a recently proposed model for water waves in 2+1 dimensions: we show that under a nonlinear time transformation, a certain reduction of this partial differential equation is mapped to an ordinary differential equation which does not have the Painlev´e property. This is in contrast to what happens in the case of the Camassa-Holm equation. Also, and again in contrast to the case of the Camassa-Holm equation, the equation under study fails to admit Dirichlet series solutions. - MSC2000 classification scheme numbers: 35Q51, 35Q58, 37K10.

Analytical approximation of cuspidal loops using a nonlinear time transformation method

2020 ◽  
Vol 373 ◽  
pp. 125042 ◽  
Author(s):  
Bo-Wei Qin ◽  
Kwok-Wai Chung ◽  
Antonio Algaba ◽  
Alejandro J. Rodríguez-Luis
Keyword(s):  
Transformation Method ◽  
Analytical Approximation ◽  
Time Transformation ◽  
Nonlinear Time Transformation

scholarly journals Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

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