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Alfvén solitons and generalized Darboux transformation for a variable-coefficient derivative nonlinear Schrödinger equation in an inhomogeneous plasma

2021; Elsevier BV; Volume: 148; Linguagem: Inglês

10.1016/j.chaos.2021.111029

1873-2887

Su‐Su Chen, Bo Tian, Qi‐Xing Qu, He Li, Yan Sun, Xia‐Xia Du,

Quantum Mechanics and Non-Hermitian Physics

Abstract Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a variable-coefficient derivative nonlinear Schrodinger equation describing the propagation of the nonlinear Alfven waves in an inhomogeneous plasma. Based on the existing Lax pair, with respect to the left polarized Alfven wave, the N -fold generalized Darboux transformation, rational one/two Alfven soliton solutions and mixed two Alfven soliton solutions are derived, where N = 1 , 2 , 3 … . For those Alfven solitons, we find that (1) the solitonic width cannot be affected by the dispersion coefficient h ( τ ) and the loss/gain coefficient f ( τ ) , where τ is the stretched space variable; the solitonic amplitude grows (or decays) in the exponential rate exp [ − ∫ f ( τ ) d τ ] ; the solitonic amplitude cannot be affected by h ( τ ) ; the solitonic velocity and trajectory are related to h ( τ ) , while they cannot be affected by f ( τ ) ; (2) the rational two Alfven solitons experience no phase shift after the interaction; (3) the modulus square of mixed two Alfven solitons can be decomposed into two single Alfven solitons with the ∫ h ( τ ) d τ -dependent phase shifts; (4) the collapse of the rational one Alfven soliton is displayed.