On integrability of a class of block-triangular evolution systems
نویسنده
چکیده
In the present paper we prove the integrability (in the sense of existence of formal symmetry of infinite rank) for a class of (1+1)-dimensional evolution systems generalizing the triangular systems considered by Bakirov, Beukers, Sanders and Wang, and by Sanders and van der Kamp. The important consequence of this result is the existence of formal symmetry of infinite rank for “almost integrable” systems, recently discovered by Sanders and van der Kamp, and for a large class of logarithmic extensions of integrable evolution systems, introduced by Kupershmidt.
منابع مشابه
On a class of inhomogeneous extensions for integrable evolution systems
In the present paper we prove the integrability (in the sense of existence of formal symmetry of infinite rank) for a class of block-triangular inhomogeneous extensions of (1+1)-dimensional integrable evolution systems. An important consequence of this result is the existence of formal symmetry of infinite rank for “almost integrable” systems, recently discovered by Sanders and van der Kamp.
متن کاملOn a class of inhomogeneous extensions for integrable evolution systems1
In the present paper we prove the integrability (in the sense of existence of formal symmetry of infinite rank) for a class of block-triangular inhomogeneous extensions of (1+1)-dimensional integrable evolution systems. An important consequence of this result is the existence of formal symmetry of infinite rank for “almost integrable” systems, recently discovered by Sanders and van der Kamp.
متن کاملRelationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
متن کاملFUZZY GOULD INTEGRABILITY ON ATOMS
In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...
متن کاملIntroduction to Schramm-Loewner evolution and its application to critical systems
In this short review we look at recent advances in Schramm-Loewner Evolution (SLE) theory and its application to critical phenomena. The application of SLE goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. Through the use of SLE, the evolution of conformally invariant paths on the complex plane can be followed; hence a...
متن کامل