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- W3201817942 abstract "Abstract This work generalizes and extends our work in refs [10,29,37], dealing a theoretical model of a monoatomic chain immersed in a potential of periodic and deformable substrate, the third and fourth non-linearities being taken into account. Looking at the analytical localized modes provides an extended interpretation of system dynamics based upon modes existence and yields an extended form of the nonlinear Schrodinger equation to describe the eikonal wave's complex amplitude. In this equation, the coeffcients depend on the wavenumber, whereas the parallel with the nonlinear transmission electrical line introduced in references results in [1,2] not fully resolved dynamic equations. So far, only specific solutions have been presented. Our dynamic study thus presents a theoretical prediction for their experimental set up. In contrast to previous works done for particular values of the wavenumber, namely on the behavior of gap ( k = 0 and k = π) solutions of the model [10], or for k ( k = ±2π=3) in the central bandpass area [37], we consider here rather behaviors of the system when the angular frequency is arbitrary. By using bifurcation theory of planar dynamical systems and investigating the dynamical behavior, we derive a variety of solutions corresponding to the phase trajectories under different parameter conditions." @default.
- W3201817942 created "2021-10-11" @default.
- W3201817942 creator A5082951485 @default.
- W3201817942 date "2021-09-20" @default.
- W3201817942 modified "2023-10-16" @default.
- W3201817942 title "Singular Nonlinear Equation Class : Theoretical and Experimental Concept" @default.
- W3201817942 doi "https://doi.org/10.21203/rs.3.rs-865335/v1" @default.
- W3201817942 hasPublicationYear "2021" @default.
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