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The Boussinesq equation and Miura-type transformations

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Several Miura-type transformations for the Boussinesq equation are found and the corresponding integrable systems are constructed.

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  1. 1.

    M. Antonowicz, A. P. Fordy, and Q. P. Liu, “Energy-dependent third-order Lax operators,” Nonlinearity, 4, 669–684 (1991).

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    A. B. Borisov, S. A. Zykov, and M. V. Pavlov, “Dressing sequences of discrete symmetries and multiplying nonlinear equations,” Teor. Mat. Fiz., 116, 199–214 (1998).

    Google Scholar 

  3. 3.

    A. B. Borisov, M. V. Pavlov, and S. A. Zykov, “Proliferation scheme for the Kaup—Boussinesq system,” Physica D, 152/153, 104–109 (2001).

    MathSciNet  Article  Google Scholar 

  4. 4.

    E. V. Ferapontov, “Differential geometry of nonlocal Hamiltonian operators of the hydrodynamical type,” Funkts. Anal. Prilozh., 25, No. 3, 37–49 (1991).

    MATH  MathSciNet  Google Scholar 

  5. 5.

    A. Ya. Maltsev and S. P. Novikov, “On the local systems Hamiltonian in the weakly nonlocal Poisson brackets,” Physica D, 156, 53–80 (2001).

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    M. V. Pavlov, “Relationships between differential substitutions and Hamiltonian structures of the Korteweg—de Vries equation,” Phys. Lett. A, 243, Nos. 5–6, 295–300 (1998).

    MATH  MathSciNet  Article  Google Scholar 

  7. 7.

    M. V. Pavlov, “Integrable systems and metrics of constant curvature,” J. Nonlin. Math. Phys., 9,Suppl. 1, 173–191 (2002).

    Google Scholar 

  8. 8.

    M. V. Pavlov and S. P. Tsarev, “Three-Hamiltonian structures for Egorov systems of the hydrodynamical type,” Funkts. Anal. Prilozh., 37. No. 1, 32–45 (2003).

    MathSciNet  Article  MATH  Google Scholar 

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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.

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Pavlov, M.V. The Boussinesq equation and Miura-type transformations. J Math Sci 136, 4478–4483 (2006).

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  • Canonical Form
  • Poisson Bracket
  • Boussinesq Equation
  • Hamiltonian Operator
  • Laurent Series