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On the Numerical Approximation to Generalized Ostrovsky Equations: II

Dynamics of Solitary-Wave Solutions
  • Ángel Durán
Chapter
Part of the Understanding Complex Systems book series (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.

Keywords

Generalized Ostrovsky equation Fourier collocation method Petviashvili-type methods Solitary waves Stability Resolution property 

Notes

Acknowledgements

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

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Mathematics DepartmentUniversity of ValladolidValladolidSpain

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