New exact compacton, peakon and solitary solutions of the generalized Boussinesq-like equations with nonlinear dispersion

Zhang, Lijun; Chen, Liqun; Huo, Xuwen

doi:10.1016/j.na.2006.10.009

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…Lemma 2 [23] Let x and y be real vectors of the same dimension. Then, for any scalar ε > 0, the following inequality holds:…”

Section: Problem Statementmentioning

confidence: 99%

A novel robust proportional-integral (PI) adaptive observer design for chaos synchronization

Pourgholi¹,

Majd²

2011

Chinese Phys. B

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In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.

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“…Lemma 2 [23] Let x and y be real vectors of the same dimension. Then, for any scalar ε > 0, the following inequality holds:…”

Section: Problem Statementmentioning

confidence: 99%

A novel robust proportional-integral (PI) adaptive observer design for chaos synchronization

Pourgholi¹,

Majd²

2011

Chinese Phys. B

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“…Abundant compactons [10][11][12][13] are developed by the Adominan decomposition method. For < 0, exact solutions with solitary patterns of Boussinesq-like ( , ) equations are obtained in the works by Shang [14] and Zhang et al [15] by extending sinh-cosh method and by using the integral approach, respectively.…”

Section: Introductionmentioning

confidence: 99%