Traveling nonsmooth solution and conserved quantities of long nonlinear internal waves

Supriya Mandal (), Prakash Kr. Das (), Debabrata Singh () and M. M. Panja ()
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Supriya Mandal: Visva-Bharati
Prakash Kr. Das: Trivenidevi Bhalotia College
Debabrata Singh: Visva-Bharati
M. M. Panja: Visva-Bharati

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 884-899

Abstract: Abstract This work deals with applying a rapidly convergent approximation method to obtain some (weak) nonsmooth solitary or periodic solutions of a generic version of the Korteweg-de Vries and the Benjamin-Bona-Mahony equations, the generalized Gardner equation with dual power-law nonlinearity. A novel approach has been adopted to derive conditions among parameters for which the obtained solution may be bounded. Explicit parameter dependence of few constants of the motion corresponding to the nonsmooth solitary or periodic solutions obtained here has been presented. Results derived here may be helpful in interpretations of large-amplitude internal waves in the ocean and for irregularly large-amplitude waves in other fields of nonlinear physics, e.g., optics and dusty- or magneto-plasmas.

Keywords: Long nonlinear internal waves; Generalized Gardner equation; Rapidly convergent approximation method; Traveling nonsmooth solution; Constant of the motion; 34A45; 35C05; 35D30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00194-6

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