Dressing for a vector modified KdV hierarchy

Panagiota-Maria Adamopoulou; Georgios Papamikos

doi:10.1007/978-3-030-55777-5_48

Dressing for a vector modified KdV hierarchy

Panagiota-Maria Adamopoulou
, Georgios Papamikos

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We present the hierarchy and soliton solutions associated with a multi-component generalisation of the modified Korteweg–de Vries equation. A recursive formula for obtaining the Lax operators associated with the higher flows of the hierarchy is provided. Using the method of rational dressing and the symmetries of the Lax operators we obtain the one-soliton solution. We also derive the general rank one-breather solution and express it in terms of determinants. We present the simplest case of the one-breather solution, which is parameterised by two constant unit vectors normal to each other. Finally, we obtain the associated Bäcklund transformation for the hierarchy.

Original language	English
Title of host publication	Quantum Theory and Symmetries
Subtitle of host publication	Proceedings of the 11th International Symposium, Montreal, Canada
Editors	Manu Paranjape, Richard MacKenzie, Zora Thomova, Pavel Winternitz, William Witczak-Krempa
Publisher	Springer
Pages	513-522
Number of pages	10
ISBN (Electronic)	9783030557775
ISBN (Print)	9783030557768
DOIs	https://doi.org/10.1007/978-3-030-55777-5_48
Publication status	Published - 8 Aug 2020

Publication series

Name	CRM Series on Mathematical Physics

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10.1007/978-3-030-55777-5_48

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Adamopoulou, P.-M., & Papamikos, G. (2020). Dressing for a vector modified KdV hierarchy. In M. Paranjape, R. MacKenzie, Z. Thomova, P. Winternitz, & W. Witczak-Krempa (Eds.), Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada (pp. 513-522). (CRM Series on Mathematical Physics). Springer. https://doi.org/10.1007/978-3-030-55777-5_48

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author = "Panagiota-Maria Adamopoulou and Georgios Papamikos",

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Dressing for a vector modified KdV hierarchy. / Adamopoulou, Panagiota-Maria; Papamikos, Georgios.
Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada. ed. / Manu Paranjape; Richard MacKenzie; Zora Thomova; Pavel Winternitz; William Witczak-Krempa. Springer, 2020. p. 513-522 (CRM Series on Mathematical Physics).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - We present the hierarchy and soliton solutions associated with a multi-component generalisation of the modified Korteweg–de Vries equation. A recursive formula for obtaining the Lax operators associated with the higher flows of the hierarchy is provided. Using the method of rational dressing and the symmetries of the Lax operators we obtain the one-soliton solution. We also derive the general rank one-breather solution and express it in terms of determinants. We present the simplest case of the one-breather solution, which is parameterised by two constant unit vectors normal to each other. Finally, we obtain the associated Bäcklund transformation for the hierarchy.

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Dressing for a vector modified KdV hierarchy

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