id sid tid token lemma pos w089280472x 1 1 we we PRON w089280472x 1 2 study study VERB w089280472x 1 3 a a DET w089280472x 1 4 family family NOUN w089280472x 1 5 of of ADP w089280472x 1 6 shallow shallow ADJ w089280472x 1 7 water water NOUN w089280472x 1 8 wave wave NOUN w089280472x 1 9 equations equation NOUN w089280472x 1 10 called call VERB w089280472x 1 11 the the DET w089280472x 1 12 b b NOUN w089280472x 1 13 - - PUNCT w089280472x 1 14 family family NOUN w089280472x 1 15 equation equation NOUN w089280472x 1 16 . . PUNCT w089280472x 2 1 known know VERB w089280472x 2 2 for for ADP w089280472x 2 3 having have VERB w089280472x 2 4 multi multi ADJ w089280472x 2 5 - - ADJ w089280472x 2 6 peakon peakon ADJ w089280472x 2 7 solutions solution NOUN w089280472x 2 8 , , PUNCT w089280472x 2 9 this this DET w089280472x 2 10 family family NOUN w089280472x 2 11 includes include VERB w089280472x 2 12 the the DET w089280472x 2 13 camassa camassa ADJ w089280472x 2 14 - - PUNCT w089280472x 2 15 holm holm NOUN w089280472x 2 16 equation equation NOUN w089280472x 2 17 and and CCONJ w089280472x 2 18 the the DET w089280472x 2 19 degasperis degasperis PROPN w089280472x 2 20 - - PUNCT w089280472x 2 21 procesi procesi PROPN w089280472x 2 22 equation equation NOUN w089280472x 2 23 as as ADP w089280472x 2 24 its its PRON w089280472x 2 25 most most ADV w089280472x 2 26 notable notable ADJ w089280472x 2 27 and and CCONJ w089280472x 2 28 only only ADV w089280472x 2 29 integrable integrable ADJ w089280472x 2 30 members member NOUN w089280472x 2 31 ( ( PUNCT w089280472x 2 32 using use VERB w089280472x 2 33 the the DET w089280472x 2 34 perturbative perturbative ADJ w089280472x 2 35 symmetry symmetry NOUN w089280472x 2 36 definition definition NOUN w089280472x 2 37 ) ) PUNCT w089280472x 2 38 . . PUNCT w089280472x 3 1 we we PRON w089280472x 3 2 show show VERB w089280472x 3 3 that that SCONJ w089280472x 3 4 the the DET w089280472x 3 5 periodic periodic ADJ w089280472x 3 6 and and CCONJ w089280472x 3 7 non non ADJ w089280472x 3 8 - - ADJ w089280472x 3 9 periodic periodic ADJ w089280472x 3 10 cauchy cauchy ADJ w089280472x 3 11 problem problem NOUN w089280472x 3 12 for for ADP w089280472x 3 13 the the DET w089280472x 3 14 b b NOUN w089280472x 3 15 - - PUNCT w089280472x 3 16 family family NOUN w089280472x 3 17 equation equation NOUN w089280472x 3 18 is be AUX w089280472x 3 19 well well ADV w089280472x 3 20 - - PUNCT w089280472x 3 21 posed pose VERB w089280472x 3 22 in in ADP w089280472x 3 23 sobolev sobolev NOUN w089280472x 3 24 spaces space NOUN w089280472x 3 25 with with ADP w089280472x 3 26 exponent exponent NOUN w089280472x 3 27 greater great ADJ w089280472x 3 28 than than ADP w089280472x 3 29 3/2 3/2 NUM w089280472x 3 30 . . PUNCT w089280472x 4 1 moreover moreover ADV w089280472x 4 2 , , PUNCT w089280472x 4 3 we we PRON w089280472x 4 4 find find VERB w089280472x 4 5 that that SCONJ w089280472x 4 6 the the DET w089280472x 4 7 corresponding correspond VERB w089280472x 4 8 data data NOUN w089280472x 4 9 - - PUNCT w089280472x 4 10 to to ADP w089280472x 4 11 - - PUNCT w089280472x 4 12 solution solution NOUN w089280472x 4 13 map map NOUN w089280472x 4 14 is be AUX w089280472x 4 15 continuous continuous ADJ w089280472x 4 16 on on ADP w089280472x 4 17 sobolev sobolev NOUN w089280472x 4 18 spaces space NOUN w089280472x 4 19 but but CCONJ w089280472x 4 20 not not PART w089280472x 4 21 uniformly uniformly ADV w089280472x 4 22 continuous continuous ADJ w089280472x 4 23 . . PUNCT w089280472x 5 1 we we PRON w089280472x 5 2 prove prove VERB w089280472x 5 3 that that SCONJ w089280472x 5 4 this this DET w089280472x 5 5 map map NOUN w089280472x 5 6 is be AUX w089280472x 5 7 not not PART w089280472x 5 8 uniformly uniformly ADV w089280472x 5 9 continuous continuous ADJ w089280472x 5 10 using use VERB w089280472x 5 11 approximate approximate ADJ w089280472x 5 12 solutions solution NOUN w089280472x 5 13 together together ADV w089280472x 5 14 with with ADP w089280472x 5 15 delicate delicate ADJ w089280472x 5 16 commutator commutator NOUN w089280472x 5 17 and and CCONJ w089280472x 5 18 multiplier multipli ADJ w089280472x 5 19 estimates estimate NOUN w089280472x 5 20 . . PUNCT w089280472x 6 1 the the DET w089280472x 6 2 novelty novelty NOUN w089280472x 6 3 of of ADP w089280472x 6 4 the the DET w089280472x 6 5 proof proof NOUN w089280472x 6 6 lies lie VERB w089280472x 6 7 in in ADP w089280472x 6 8 the the DET w089280472x 6 9 fact fact NOUN w089280472x 6 10 that that SCONJ w089280472x 6 11 it it PRON w089280472x 6 12 makes make VERB w089280472x 6 13 no no DET w089280472x 6 14 use use NOUN w089280472x 6 15 of of ADP w089280472x 6 16 conserved conserved ADJ w089280472x 6 17 quantities quantity NOUN w089280472x 6 18 . . PUNCT w089280472x 7 1 lastly lastly ADV w089280472x 7 2 , , PUNCT w089280472x 7 3 given give VERB w089280472x 7 4 a a DET w089280472x 7 5 weaker weak ADJ w089280472x 7 6 topology topology NOUN w089280472x 7 7 , , PUNCT w089280472x 7 8 we we PRON w089280472x 7 9 show show VERB w089280472x 7 10 that that SCONJ w089280472x 7 11 the the DET w089280472x 7 12 data data NOUN w089280472x 7 13 - - PUNCT w089280472x 7 14 to to ADP w089280472x 7 15 - - PUNCT w089280472x 7 16 solution solution NOUN w089280472x 7 17 map map NOUN w089280472x 7 18 is be AUX w089280472x 7 19 holder holder NOUN w089280472x 7 20 continuous continuous ADJ w089280472x 7 21 . . PUNCT