Geodesic
QUASIINVARIANT GAUSSIAN MEASURES FOR ONE-DIMENSIONAL HAMILTONIAN PARTIAL DIFFERENTIAL EQUATIONS
Forum of Mathematics, Sigma, Tome 3 (2015)

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We prove the quasiinvariance of Gaussian measures (supported by functions of increasing Sobolev regularity) under the flow of one-dimensional Hamiltonian partial differential equations such as the regularized long wave, also known as the Benjamin–Bona–Mahony (BBM) equation. 
@article{10_1017_fms_2015_27,
     author = {NIKOLAY TZVETKOV},
     title = {QUASIINVARIANT {GAUSSIAN} {MEASURES} {FOR} {ONE-DIMENSIONAL} {HAMILTONIAN} {PARTIAL} {DIFFERENTIAL} {EQUATIONS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {3},
     year = {2015},
     doi = {10.1017/fms.2015.27},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2015.27/}
}
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NIKOLAY TZVETKOV. QUASIINVARIANT GAUSSIAN MEASURES FOR ONE-DIMENSIONAL HAMILTONIAN PARTIAL DIFFERENTIAL EQUATIONS. Forum of Mathematics, Sigma, Tome 3 (2015). doi: 10.1017/fms.2015.27

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