In this paper, we revisit the standard derivative NLS equation and investigate two nonlocal integrable derivative NLS equations via the IST. Furthermore, depending on the adoptedĪssumptions and the chosen governing equations, each approach may provideĭifferent values for the corresponding dispersive and nonlinear coefficients. The derivative NLS equation is an important nonlinear dispersive equation, which arises in many different contexts. On how the variables are interpreted physically, the resulting NLSE can model aĭifferent dynamics of the wave packet. Multiple-scale from other mathematical models as governing equations. The former featuresĭerivations of the NLSE heuristically and by employing the method of The modeling aspect of the NLSE but also provides an overview of theĪpplications in these four exciting research areas. Superconductivity, nonlinear optics, and BEC. Of applications, including but not limited to, surface gravity waves, This nonlinearĮvolution equation arises in various physical settings and admits a wide range Integrable systems of a nonlinear partial differential equation (PDE) in $(1 +ġ)$D and it possesses an infinite set of conservation laws. Referred to as the Gross-Pitaevskii equation (GPE). In the context of Bose-Einstein condensate (BEC), it is often Karjanto Download PDF Abstract: The nonlinear Schrödinger equation (NLSE) models the slowly varyingĮnvelope dynamics of a weakly nonlinear quasi-monochromatic wave packet inĭispersive media. Download a PDF of the paper titled The nonlinear Schr\"odinger equation: A mathematical model with its wide-ranging applications, by N.
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