Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infinite series and variational formulations

Gaetana Gambino, Tanriver, Roy Choudhury

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Abstract

In this paper we employ three recent analytical approaches to investigate severalclasses of traveling wave solutions of the so-called extended-reduced OstrovskyEquation (exROE). A recent extension of phase-plane analysis is first employedto show the existence of breaking kink wave solutions and smooth periodic wave(compacton) solutions. Next, smooth traveling waves are derived using a recenttechnique to derive convergent multi-infinite series solutions for the homoclinic orbitsof the traveling-wave equations for the exROE equation. These correspond topulse solutions respectively of the original PDEs. We perform many numerical testsin different parameter regime to pinpoint real saddle equilibrium points of the correspondingtraveling-wave equations, as well as ensure simultaneous convergence andcontinuity of the multi-infinite series solutions for the homoclinic orbits anchoredby these saddle points. Unlike the majority of unaccelerated convergent series, highaccuracy is attained with relatively few terms. And finally, variational methods areemployed to generate families of both regular and embedded solitary wave solutionsfor the exROE PDE. The technique for obtaining the embedded solitons incorporatesseveral recent generalizations of the usual variational technique and it is thustopical in itself. One unusual feature of the solitary waves derived here is that weare able to obtain them in analytical form (within the assumed ansatz for the trialfunctions). Thus, a direct error analysis is performed, showing the accuracy of theresulting solitary waves. Given the importance of solitary wave solutions in wavedynamics and information propagation in nonlinear PDEs, as well as the fact thatnot much is known about solutions of the family of generalized exROE equationsconsidered here, the results obtained are both new and timely
Lingua originaleEnglish
pagine (da-a)85-100
Numero di pagine16
RivistaAN INTERDISCIPLINARY JOURNAL OF DISCONTINUITY, NONLINEARITY, AND COMPLEXITY
Volume5
Stato di pubblicazionePublished - 2016

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

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