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Solitons, multi-solitons and multi-periodic solutions of the generalized Lax equation by Darboux transformation and its quasiperiodic motions.

Authors :
Pal, Nanda Kanan
Chatterjee, Prasanta
Saha, Asit
Source :
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics. 12/10/2024, Vol. 38 Issue 30, p1-19. 19p.
Publication Year :
2024

Abstract

Using the Darboux transformation method, the general Lax equation is solved and a collection of new exact solutions together with one-soliton solutions, singular one-soliton solutions, periodic solutions, singular periodic solution, two-soliton solutions, singular two-soliton solutions, two-periodic solutions and singular two-periodic solutions is obtained. Using traveling wave transformation, the Lax equation is transfigured to a conservative dynamical system (CDS) of dimension four with three equilibrium points involving two parameters γ and v. The CDS has various quasi-periodic motions for fixed values of the parameters γ and v at different initial conditions. Furthermore, effects of the parameters γ and v are shown on the quasiperiodic motions of the CDS by means of phase sections and time series plots. This approach can be applied to a heterogeneity of nonlinear model equations or partial differential equations for describing their inherent nonlinear phenomena. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02179792
Volume :
38
Issue :
30
Database :
Academic Search Index
Journal :
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics
Publication Type :
Academic Journal
Accession number :
179551513
Full Text :
https://doi.org/10.1142/S0217979224400010