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Whitham modulation theory for the Kadomtsev- Petviashvili equation.

ABSTRACT: The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

SUBMITTER: Ablowitz MJ

PROVIDER: S-EPMC5582171 | biostudies-literature | 2017 Aug

REPOSITORIES: biostudies-literature

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Whitham modulation theory for the Kadomtsev- Petviashvili equation.

Ablowitz Mark J MJ Biondini Gino G Wang Qiao Q

Proceedings. Mathematical, physical, and engineering sciences 20170802 2204

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solut ...[more]

PMID: 28878550

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Project description:BACKGROUND:Understanding factors that affect dental attendance behavior helps in constructing effective oral health campaigns. A socio-cognitive model that adequately explains variance in regular dental attendance has yet to be validated among younger adults in Norway. Focusing a representative sample of younger Norwegian adults, this cross-sectional study provided an empirical test of the Theory of Planned Behavior (TPB) augmented with descriptive norm and action planning and estimated direct and indirect effects of attitudes, subjective norms, descriptive norms, perceived behavioral control and action planning on intended and self-reported regular dental attendance. METHOD:Self-administered questionnaires provided by 2551, 25-35 year olds, randomly selected from the Norwegian national population registry were used to assess socio-demographic factors, dental attendance as well as the constructs of the augmented TPB model (attitudes, subjective norms, descriptive norms, intention, action planning). A two-stage process of structural equation modelling (SEM) was used to test the augmented TPB model. RESULTS:Confirmatory factor analysis, CFA, confirmed the proposed correlated 6-factor measurement model after re-specification. SEM revealed that attitudes, perceived behavioral control, subjective norms and descriptive norms explained intention. The corresponding standardized regression coefficients were respectively (??=?0.70), (? =0.18), (??=?-?0.17) and (? =0.11) (p?<?0.001). Intention (? =0.46) predicted action planning and action planning (? =0.19) predicted dental attendance behavior (p?<?0.001). The model revealed indirect effects of intention and perceived behavioral control on behavior through action planning and through intention and action planning, respectively. The final model explained 64 and 41% of the total variance in intention and dental attendance behavior. CONCLUSION:The findings support the utility of the TPB, the expanded normative component and action planning in predicting younger adults' intended- and self-reported dental attendance. Interventions targeting young adults' dental attendance might usefully focus on positive consequences following this behavior accompanied with modeling and group performance.

Dataset Information

Whitham modulation theory for the Kadomtsev- Petviashvili equation.

Publications

Whitham modulation theory for the Kadomtsev- Petviashvili equation.

Similar Datasets

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