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Exact two-soliton solutions and two-periodic solutions of the perturbed mKdV equation with variable coefficients

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Abstract

We discuss the Darboux transformation method for a modified Korteweg–de Vries equation with variable coefficients and perturbing terms in detail based on the general form of the Darboux transformations for some nonlinear evolution equations solvable by the Ablowitz–Kaup–Newell–Segur inverse scattering method. We use this method to generate families of two-soliton solutions and two-periodic solutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chuxiong Normal University, Chuxiong, China

    Ying Huang & Lin Liang

Authors
  1. Ying Huang
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  2. Lin Liang
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Correspondence to Ying Huang.

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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 2, pp. 244–252, August, 2015.

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Huang, Y., Liang, L. Exact two-soliton solutions and two-periodic solutions of the perturbed mKdV equation with variable coefficients. Theor Math Phys 184, 1106–1113 (2015). https://doi.org/10.1007/s11232-015-0320-0

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  • DOI: https://doi.org/10.1007/s11232-015-0320-0

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