Non‐auto Darboux transformation for N‐soliton solutions of the non‐isospectral Korteweg–de Vries hierarchy

The usual non‐isospectral Korteweg–de Vries (KdV) hierarchy (see Equation 4) does not have auto Darboux transformations. In this paper, we present a non‐auto Darboux transformation for this hierarchy, from which we are able to construct its N$$ N $$‐soliton solutions. An explicit formula of the solu...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-06, Vol.47 (9), p.7518-7531
Main Authors: Liu, Xing‐yu, Lu, Bin‐he, Zhang, Da‐jun
Format: Article
Language:English
Subjects:
Darboux transformation
Korteweg–de Vries equation
Miura transformation
non‐isospectral hierarchy
Solitary waves
solution
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Summary:The usual non‐isospectral Korteweg–de Vries (KdV) hierarchy (see Equation 4) does not have auto Darboux transformations. In this paper, we present a non‐auto Darboux transformation for this hierarchy, from which we are able to construct its N$$ N $$‐soliton solutions. An explicit formula of the solutions with zero background is given, and solutions are illustrated.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9986