THERMAL SCIENCE

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Sheng Zhang

,

Caihong You

INVERSE SCATTERING TRANSFORM FOR NEW MIXED SPECTRAL ABLOWITZ-KAUP-NEWELL-SEGUR EQUATIONS

ABSTRACT
The inverse scattering transform plays a very important role in promoting the development of analytical methods to solve non-linear PDE exactly. In this paper, new and more general mixed spectral Ablowitz-Kaup-Newell-Segur equations are derived and solved by embedding a novel time-varying spectral parameter in-to an associated linear problem and the inverse scattering transform. As a result, new exact solutions and n-soliton solutions are obtained. To gain more insights into the embedded spectral parameter and the obtained solutions, some dynamical evolutions, and spatial structures are simulated. It is shown that the derived Ablowitz-Kaup-Newell-Segur equations are Lax integrable and the obtained soliton solutions possess time-varying amplitudes.
KEYWORDS
mixed spectral Ablowitz-Kaup-Newell-Segur equations, inverse scattering transform, n-soliton solution, dynamical evolution, spatial structure, Lax integrability
PAPER SUBMITTED: 2018-04-28
PAPER REVISED: 2019-09-01
PAPER ACCEPTED: 2019-09-08
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004437Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 4, PAGES [2437 - 2444]
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Inverse scattering transform for new mixed spectral Ablowitz-Kaup-Newell-Segur equations

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