《Communications in Theoretical Physics》 2017年07期

# Invariant Functions, Symmetries and Primary Branch Solutions of First Order Autonomous Systems

【摘要】：An invariant function(IF) is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary(1+1)-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.

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