Nonlocal symmetries and new interaction waves of the variable-coefficient modified Korteweg–de Vries equation in fluid-filled elastic tubes

The Lax pair is developed to construct nonlocal symmetries of the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation in fluid-filled elastic tubes. To construct new exact solutions with the nonlocal symmetry, we use the localization approach, which can transform the problem of nonloc...

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Bibliographic Details
Published in:European physical journal plus Vol. 137; no. 7; p. 814
Main Authors: Wu, Jian-Wen, He, Jun-Tao, Lin, Ji
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Springer Nature B.V
Subjects:
Applied and Technical Physics
Atomic
Cnoidal waves
Complex Systems
Condensed Matter Physics
Exact solutions
Korteweg-Devries equation
Lie groups
Localization
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Solitary waves
Symmetry
Theoretical
Tubes
ISSN:2190-5444, 2190-5444
Online Access:Get full text
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Summary:The Lax pair is developed to construct nonlocal symmetries of the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation in fluid-filled elastic tubes. To construct new exact solutions with the nonlocal symmetry, we use the localization approach, which can transform the problem of nonlocal symmetries to Lie point symmmetries. Furthermore, using the classic Lie group reduction method some group invariant solutions of the vc-mKdV equation are obtained. For some interesting solutions, the soliton-cnoidal waves are discussed through the graphical analysis.
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ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-022-03033-7