Solitary waves with the Madelung fluid description: a generalized derivative nonlinear Schrödinger equation
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Lü, Xing
Ma, Wen-Xiu
Yu, Jun
Khalique, Chaudry Masood
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Elsevier
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WithintheframeworkoftheMadelungfluiddescription,wewillderivebrightanddark(includinggray-andblack-soliton)envelopesolutionsforageneralizedderivativenonlin-earSchrödingermodeli∂ ∂t=∂2 ∂x2+ia∂∂x(| |2 )+b| |2 ,byvirtueofthecorrespondingsolitarywavesolutionsforthestationaryGardnerequations.Notethatweonlyconsiderthemotionwithstationary-profilecurrentvelocitycaseandexcludethemotionwithconstantcurrentvelocitycasefora =0;ontheotherhand,ourresultsarederivedundersuitableas-sumptionsforthecurrentvelocityassociatedwithcorrespondingboundaryconditionsofthefluiddensity,andundercorrespondingparametricconstraints.
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Lü, X. et al. 2016. Solitary waves with the Madelung fluid description: a generalized derivative nonlinear Schrödinger equation. Communications in Nonlinear Science and Numerical Simulation, 31:40-46. [https://doi.org/10.1016/j.cnsns.2015.07.007]