Geodesic
Nonrelativistic Limit of the Bosonic String
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 198-209

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An action for the nonrelativistic string is proposed that is invariant under general coordinate transformations on the string worldsheet. Hamiltonian formalism for the nonrelativistic string is given. Particular solutions of the Euler–Lagrange equations are found in the time gauge. 
@article{TM_2020_309_a12,
     author = {M. O. Katanaev},
     title = {Nonrelativistic {Limit} of the {Bosonic} {String}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {198--209},
     publisher = {mathdoc},
     volume = {309},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_309_a12/}
}
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M. O. Katanaev. Nonrelativistic Limit of the Bosonic String. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 198-209. http://geodesic.mathdoc.fr/item/TM_2020_309_a12/