Schwarzian KP is recast as an integral bilinear equation on pairs of KP tau-functions, yielding Harry Dym via Lax-Sato and an embedding into multi-component KP.
Integrable Hierarchies and Dispersionless Limit
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abstract
Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of the ordinary KP and Toda hierarchy. An alternative construction of general solutions of the ordinary KP and Toda hierarchy is given as twistor construction which is quatization of the similar construction of solutions of dispersionless hierarchies. These results as well as those obtained in previous papers are presented with proofs and necessary technical details.
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UNVERDICTED 2representative citing papers
Revisits Bäcklund-Darboux transformations for KP, BKP and related hierarchies in bilinear tau-function and fermionic operator frameworks, extending naturally to fully discrete cases.
citing papers explorer
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Bilinear formalism for Schwarzian KP and Harry Dym hierarchies
Schwarzian KP is recast as an integral bilinear equation on pairs of KP tau-functions, yielding Harry Dym via Lax-Sato and an embedding into multi-component KP.
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Revisiting B\"acklund-Darboux transformations for KP and BKP integrable hierarchies
Revisits Bäcklund-Darboux transformations for KP, BKP and related hierarchies in bilinear tau-function and fermionic operator frameworks, extending naturally to fully discrete cases.