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Traveling wave solutions of the derivative nonlinear Schrödinger hierarchy

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  • Kudryashov, Nikolay A.
  • Lavrova, Sofia F.

Abstract

The first three members of the nonlinear ordinary differential equations for the derivative nonlinear Schrödinger hierarchy are considered. Reduction to nonlinear ordinary differential equations is utilized to obtain traveling wave solutions. Lax pairs for these nonlinear ordinary differential equations are presented. The first integrals of nonlinear ordinary differential equations are obtained by taking Lax pairs into account. Exact solutions in the form of solitary and periodic waves are found by means of the generalized method of auxiliary equations.

Suggested Citation

  • Kudryashov, Nikolay A. & Lavrova, Sofia F., 2024. "Traveling wave solutions of the derivative nonlinear Schrödinger hierarchy," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    • Handle: RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002637
    DOI: 10.1016/j.amc.2024.128802
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    References listed on IDEAS

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    1. Kudryashov, Nikolay A., 2019. "Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 323-330.
    2. Kudryashov, Nikolai A., 2005. "Fuchs indices and the first integrals of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 591-603.
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