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