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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 Schrödinger equation describing the nonlinear Alfvén waves in an inhomogeneous plasma. With respect to the left polarized Alfvén wave, the odd‐fold Darboux transformation, breather, rogue‐wave and semirational solutions are...
Nonlinear optics plays a central role in the advancement of optical science and laser‐based technologies. The second‐order rogue‐wave solutions and modulation instability for the coherently coupled nonlinear Schrödinger equations with the positive coherent coupling in nonlinear optics are reported in this paper. Generalized Darboux transformations for such coupled equations are derived, with which...
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