Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma |
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Authors: | Yong-Yan Wang Xue-Qing Liu Jian-Guang Li |
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Institution: | College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao, China. |
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Abstract: | Under investigation in this paper is an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma. Lax pair, bilinear forms, and bilinear Bäcklund transformations are derived. Based on the bilinear forms, the first-, second-, and third-order nonautonomous soliton solutions are derived. Propagation and interaction of the nonautonomous solitons are investigated and influence of the variable coefficients is also discussed: Amplitude of the first-order nonautonomous soliton is determined by the spectral parameter and perturbed factor; there exist two kinds of the solitons, namely the elevation and depression solitons, depending on the sign of the spectral parameter; the background where the nonautonomous soliton exists is influenced by the perturbed factor and external force coefficient; breather solutions can be constructed under the conjugate condition, and period of the breather is related to the dispersive and nonuniform coefficients. |
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