Integrating evolution equations using Fredholm determinants

Feride Tığlay; Feride Tığlay

doi:10.3934/era.2020109

Electronic Research Archive

2021, Volume 29, Issue 2: 2141-2147. doi: 10.3934/era.2020109

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Integrating evolution equations using Fredholm determinants

Feride Tığlay ^,

Ohio State University, Newark, 1179 University Drive, Newark, OH 43055, USA

Received: 01 January 2020 Revised: 01 August 2020 Published: 19 October 2020
Primary:35M13, 35C15;Secondary:37K10

We outline the construction of special functions in terms of Fredholm determinants to solve boundary value problems of the string spectral problem. Our motivation is that the string spectral problem is related to the spectral equations in Lax pairs of at least three nonlinear evolution equations from mathematical physics.
- Evolution equations,
- Fredholm determinants,
- integrability,
- Hunter-Saxton equation
Citation: Feride Tığlay. Integrating evolution equations using Fredholm determinants[J]. Electronic Research Archive, 2021, 29(2): 2141-2147. doi: 10.3934/era.2020109

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Abstract

We outline the construction of special functions in terms of Fredholm determinants to solve boundary value problems of the string spectral problem. Our motivation is that the string spectral problem is related to the spectral equations in Lax pairs of at least three nonlinear evolution equations from mathematical physics.

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