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On the Numerical Approximation to Generalized Ostrovsky Equations: II

Dynamics of Solitary-Wave Solutions

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Nonlinear Systems, Vol. 1

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

In this chapter generalized versions of the Ostrovsky equations are considered. These were shown to admit classical and generalized solitary wave solutions. The periodic initial-value problem for the equations is numerically solved with a fully discrete scheme based on pseudospectral discretization in space and a fourth-order composition Runge-Kutta method as time integrator. The resulting scheme is checked and applied to study numerically the dynamics of the solitary wave solutions. Specifically, we analyze the stability of classical and generalized solitary waves under small perturbations, the resolution of initial data into several solitary pulses (the so-called resolution property) and various aspects of the interaction of the solitary waves.

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Acknowledgements

This work was supported by Spanish Ministerio de Economía y Competitividad under the Research Grant MTM2014-54710-P.

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Authors and Affiliations

  1. Applied Mathematics Department, University of Valladolid, 47011, Valladolid, Spain

    Ángel Durán

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  1. Ángel Durán
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Correspondence to Ángel Durán .

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Editors and Affiliations

  1. Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain

    Victoriano Carmona

  2. Departamento de Física Aplicada I, Universidad de Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  3. Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain

    Fernando Fernández-Sánchez

  4. Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain

    Elisabeth García- Medina

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Durán, Á. (2018). On the Numerical Approximation to Generalized Ostrovsky Equations: II. In: Carmona, V., Cuevas-Maraver, J., Fernández-Sánchez, F., García- Medina, E. (eds) Nonlinear Systems, Vol. 1. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-66766-9_13

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