id sid tid token lemma pos rx913n23n21 1 1 in in ADP rx913n23n21 1 2 this this DET rx913n23n21 1 3 thesis thesis NOUN rx913n23n21 1 4 we we PRON rx913n23n21 1 5 study study VERB rx913n23n21 1 6 the the DET rx913n23n21 1 7 riemannian riemannian ADJ rx913n23n21 1 8 geometry geometry NOUN rx913n23n21 1 9 of of ADP rx913n23n21 1 10 diffeomorphism diffeomorphism NOUN rx913n23n21 1 11 groups group NOUN rx913n23n21 1 12 equipped equip VERB rx913n23n21 1 13 with with ADP rx913n23n21 1 14 a a DET rx913n23n21 1 15 variety variety NOUN rx913n23n21 1 16 of of ADP rx913n23n21 1 17 sobolev sobolev NOUN rx913n23n21 1 18 - - PUNCT rx913n23n21 1 19 type type NOUN rx913n23n21 1 20 metrics metric NOUN rx913n23n21 1 21 . . PUNCT rx913n23n21 2 1 most most ADV rx913n23n21 2 2 notably notably ADV rx913n23n21 2 3 , , PUNCT rx913n23n21 2 4 we we PRON rx913n23n21 2 5 consider consider VERB rx913n23n21 2 6 the the DET rx913n23n21 2 7 group group NOUN rx913n23n21 2 8 of of ADP rx913n23n21 2 9 volume volume NOUN rx913n23n21 2 10 - - PUNCT rx913n23n21 2 11 preserving preserve VERB rx913n23n21 2 12 diffeomorphisms diffeomorphism NOUN rx913n23n21 2 13 equipped equip VERB rx913n23n21 2 14 with with ADP rx913n23n21 2 15 a a DET rx913n23n21 2 16 weak weak ADJ rx913n23n21 2 17 l^2 l^2 NOUN rx913n23n21 2 18 metric metric ADJ rx913n23n21 2 19 , , PUNCT rx913n23n21 2 20 whose whose DET rx913n23n21 2 21 geodesics geodesic NOUN rx913n23n21 2 22 correspond correspond VERB rx913n23n21 2 23 to to ADP rx913n23n21 2 24 lagrangian lagrangian ADJ rx913n23n21 2 25 solutions solution NOUN rx913n23n21 2 26 to to ADP rx913n23n21 2 27 the the DET rx913n23n21 2 28 euler euler PROPN rx913n23n21 2 29 equations equation NOUN rx913n23n21 2 30 . . PUNCT rx913n23n21 3 1 a a DET rx913n23n21 3 2 well well ADV rx913n23n21 3 3 known know VERB rx913n23n21 3 4 result result NOUN rx913n23n21 3 5 of of ADP rx913n23n21 3 6 ebin ebin NOUN rx913n23n21 3 7 and and CCONJ rx913n23n21 3 8 marsden marsden PROPN rx913n23n21 3 9 states state VERB rx913n23n21 3 10 that that SCONJ rx913n23n21 3 11 lagrangian lagrangian ADJ rx913n23n21 3 12 solutions solution NOUN rx913n23n21 3 13 to to ADP rx913n23n21 3 14 the the DET rx913n23n21 3 15 euler euler PROPN rx913n23n21 3 16 equations equation NOUN rx913n23n21 3 17 , , PUNCT rx913n23n21 3 18 when when SCONJ rx913n23n21 3 19 framed frame VERB rx913n23n21 3 20 as as ADP rx913n23n21 3 21 an an DET rx913n23n21 3 22 initial initial ADJ rx913n23n21 3 23 value value NOUN rx913n23n21 3 24 problem problem NOUN rx913n23n21 3 25 , , PUNCT rx913n23n21 3 26 are be AUX rx913n23n21 3 27 exactly exactly ADV rx913n23n21 3 28 as as ADV rx913n23n21 3 29 smooth smooth ADJ rx913n23n21 3 30 as as ADP rx913n23n21 3 31 their their PRON rx913n23n21 3 32 initial initial ADJ rx913n23n21 3 33 conditions condition NOUN rx913n23n21 3 34 . . PUNCT rx913n23n21 4 1 we we PRON rx913n23n21 4 2 investigate investigate VERB rx913n23n21 4 3 a a DET rx913n23n21 4 4 similar similar ADJ rx913n23n21 4 5 regularity regularity NOUN rx913n23n21 4 6 property property NOUN rx913n23n21 4 7 for for ADP rx913n23n21 4 8 lagrangian lagrangian ADJ rx913n23n21 4 9 solutions solution NOUN rx913n23n21 4 10 to to ADP rx913n23n21 4 11 the the DET rx913n23n21 4 12 euler euler PROPN rx913n23n21 4 13 equations equation NOUN rx913n23n21 4 14 when when SCONJ rx913n23n21 4 15 framed frame VERB rx913n23n21 4 16 as as ADP rx913n23n21 4 17 a a DET rx913n23n21 4 18 two two NUM rx913n23n21 4 19 - - PUNCT rx913n23n21 4 20 point point NOUN rx913n23n21 4 21 boundary boundary ADJ rx913n23n21 4 22 value value NOUN rx913n23n21 4 23 problem problem NOUN rx913n23n21 4 24 . . PUNCT rx913n23n21 5 1 in in ADP rx913n23n21 5 2 particular particular ADJ rx913n23n21 5 3 , , PUNCT rx913n23n21 5 4 we we PRON rx913n23n21 5 5 prove prove VERB rx913n23n21 5 6 that that SCONJ rx913n23n21 5 7 these these DET rx913n23n21 5 8 l^2 l^2 NOUN rx913n23n21 5 9 geodesics geodesic NOUN rx913n23n21 5 10 are be AUX rx913n23n21 5 11 exactly exactly ADV rx913n23n21 5 12 as as ADV rx913n23n21 5 13 smooth smooth ADJ rx913n23n21 5 14 as as ADP rx913n23n21 5 15 their their PRON rx913n23n21 5 16 boundary boundary ADJ rx913n23n21 5 17 conditions condition NOUN rx913n23n21 5 18 . . PUNCT rx913n23n21 6 1 we we PRON rx913n23n21 6 2 achieve achieve VERB rx913n23n21 6 3 like like ADP rx913n23n21 6 4 results result NOUN rx913n23n21 6 5 in in ADP rx913n23n21 6 6 an an DET rx913n23n21 6 7 array array NOUN rx913n23n21 6 8 of of ADP rx913n23n21 6 9 other other ADJ rx913n23n21 6 10 settings setting NOUN rx913n23n21 6 11 including include VERB rx913n23n21 6 12 3d 3d PRON rx913n23n21 6 13 axisymmetric axisymmetric ADJ rx913n23n21 6 14 ideal ideal ADJ rx913n23n21 6 15 fluids fluid NOUN rx913n23n21 6 16 , , PUNCT rx913n23n21 6 17 symplectic symplectic ADJ rx913n23n21 6 18 euler euler NOUN rx913n23n21 6 19 equations equation NOUN rx913n23n21 6 20 , , PUNCT rx913n23n21 6 21 euler euler ADJ rx913n23n21 6 22 - - PUNCT rx913n23n21 6 23 alpha alpha NOUN rx913n23n21 6 24 equations equation NOUN rx913n23n21 6 25 , , PUNCT rx913n23n21 6 26 and and CCONJ rx913n23n21 6 27 one one NUM rx913n23n21 6 28 dimensional dimensional ADJ rx913n23n21 6 29 integrable integrable ADJ rx913n23n21 6 30 systems system NOUN rx913n23n21 6 31 including include VERB rx913n23n21 6 32 the the DET rx913n23n21 6 33 mu mu PROPN rx913n23n21 6 34 - - PUNCT rx913n23n21 6 35 ch ch NOUN rx913n23n21 6 36 and and CCONJ rx913n23n21 6 37 hunter hunter NOUN rx913n23n21 6 38 - - PUNCT rx913n23n21 6 39 saxton saxton NOUN rx913n23n21 6 40 equations equation NOUN rx913n23n21 6 41 . . PUNCT