Airy Kernel Determinant Solutions to the KdV Equation and Integro-Differential Painlevé Equations
(2021) Communications in Mathematical Physics — Vol. 386, n° 2, p. 1107-1153 (2021)
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- Authors
Cafasso, Mattia 
Ruzza, Giulio
- Abstract
- We study a family of unbounded solutions to the Korteweg–de Vries equation which can be constructed as log-derivatives of deformed Airy kernel Fredholm determinants, and which are connected to an integro-differential version of the second Painlevé equation. The initial data of the Korteweg–de Vries solutions are well-defined for x> 0 , but not for x[removed] 0 they involve an integro-differential analogue of the Painlevé V equation. A special case of our results yields improved estimates for the tails of the narrow wedge solution to the Kardar–Parisi–Zhang equation.
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Citations
Cafasso, M., Claeys, T., & Ruzza, G. (2021). Airy Kernel Determinant Solutions to the KdV Equation and Integro-Differential Painlevé Equations. Communications in Mathematical Physics, 386(2), 1107-1153. https://doi.org/10.1007/s00220-021-04108-9 (Original work published 2021)