https://doi.org/10.1140/epjp/s13360-022-03033-7
Regular Article
Nonlocal symmetries and new interaction waves of the variable-coefficient modified Korteweg–de Vries equation in fluid-filled elastic tubes
Department of Physics, Zhejiang Normal University, 321004, Jinhua, China
Received:
16
January
2022
Accepted:
3
July
2022
Published online:
14
July
2022
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
