ather ▁remark ably ) ▁the ▁Hunter – Sa xt on ▁equation ▁ar ises ▁in ▁this ▁context ▁too , ▁but ▁in ▁a ▁different ▁way . ▁ ▁Vari ational ▁structures ▁and ▁integra b ility ▁▁ ▁The ▁integra b ility ▁of ▁the ▁Hunter – Sa xt on ▁equation , ▁or , ▁more ▁precisely , ▁that ▁of ▁its ▁x ▁derivative ▁ ▁was ▁shown ▁by ▁Hunter ▁and ▁Zh eng , ▁who ▁explo ited ▁that ▁this ▁equation ▁is ▁obtained ▁from ▁the ▁Cam assa – Hol m ▁equation ▁ ▁in ▁the ▁" high ▁frequency ▁limit " ▁ ▁App lying ▁this ▁limit ing ▁procedure ▁to ▁a ▁L agr ang ian ▁for ▁the ▁Cam assa – Hol m ▁equation , ▁they ▁obtained ▁a ▁L agr ang ian ▁ ▁which ▁produces ▁the ▁Hunter – Sa xt on ▁equation ▁after ▁elim ination ▁of ▁v ▁and ▁w ▁from ▁the ▁E uler – L ag range ▁equations ▁for ▁u , ▁v , ▁w . ▁Since ▁there ▁is ▁also ▁the ▁more ▁obvious ▁L agr ang ian ▁ ▁the ▁Hunter – Sa xt on ▁has ▁two ▁in equ ivalent ▁vari ational ▁structures . ▁Hunter ▁and ▁Zh eng ▁also ▁obtained ▁a ▁bi h amilton ian ▁form ulation ▁and ▁a ▁La x ▁pair ▁from ▁the ▁corresponding ▁structures ▁for ▁the ▁Cam assa – Hol m ▁equation ▁in ▁a ▁similar ▁way . ▁ ▁The ▁fact ▁that ▁the ▁Hunter – Sa xt on ▁equation ▁ar ises ▁phys ically ▁in ▁two ▁different ▁ways ▁( as ▁shown ▁above ) ▁was ▁used ▁by ▁Al ì ▁and ▁Hunter ▁to ▁explain ▁why ▁it ▁has ▁this ▁b ivari ational