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Solitons of the complex modified Korteweg–de Vries hierarchy

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  • Kudryashov, Nikolay A.

Abstract

The first three members of the complex modified Korteweg–de Vries hierarchy are studied. Using the AKNS scheme, we present Lax pairs for these equations and discuss that the Cauchy problems for them can be solved by the inverse scattering transform. Solitons for the first three members of the hierarchy are looked for using the Hirota method. Two difficulties appear in applying the Hirota method to the higher-order equations of the complex modified Korteweg–de Vries hierarchy. They lie in the representation of the original equation through the Hirota operator and in the decomposition of the resulting equation into a system of equations. Overcoming these difficulties makes it possible to find one - and two-soliton solutions of the fifth and seventh order equations from the complex modified Korteweg–de Vries hierarchy. Multi-soliton solutions for other members of the hierarchy are discussed.

Suggested Citation

  • Kudryashov, Nikolay A., 2024. "Solitons of the complex modified Korteweg–de Vries hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005629
    DOI: 10.1016/j.chaos.2024.115010
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