• Commutation and Darboux transformation

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      https://www.ias.ac.in/article/fulltext/pram/085/05/0869-0880

    • Keywords

       

      Darboux transformation; nonlinear evolution equations; exact solutions.

    • Abstract

       

      In this paper we show that the Darboux transformation for a large class of nonlinear evolution equations arises due to factorization and commutation. The factorization and commutation has been pointed out earlier for Schrödinger operator. We show that it extends to a large class of nonlinear differential equations which admit Lax pairs including Boussinesq, Davey–Stewartson, Bogoyavlensky–Schiff and 𝑛-wave interaction equation.

    • Author Affiliations

       

      M V Prabhakar1 H Bhate2

      1. College of Military Engineering, Pune 411 031, India
      2. Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, India
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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