اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSymmetric Hamiltonian of the Garnier system and its degenerate systems in two variables
61
0
0.0
(
0
)
تأليف
Yusuke Sasano
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present {it symmetric Hamiltonians} for the degenerate Garnier systems in two variables. For these symmetric Hamiltonians, we make the symmetry and holomorphy conditions, and we also make a generalization of these systems involving symmetry and holomorphy conditions inductively. We also show the confluence process among each system by taking the coupling confluence process of the Painleve systems.
قيم البحث
اقرأ أيضاً
We remark on the Garnier system in two variables.
In this note, we will compare the Garnier system in two variables with four-dimensional partial differential system in two variables with $W(D_6^{(1)})$-symmetry. Both systems are different in each compactification in the variables $q_1,q_2$, however
, has same five holomorphy conditions in the variables $p_1,p_2$.
We find a one-parameter family of polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry. We also show that this system can be obtained by the compatibility conditions for the linear differential equations in three variables. W
e give a relation between it and the second member of the second Painleve hierarchy. Moreover, we give some relations between an autonomous version of its polynomial Hamiltonian system in two variables and the mKdV hierarchies.
We construct solutions of analogues of the nonstationary Schrodinger equation corresponding to the polynomial isomonodromic Hamiltonian Garnier system with two degrees of freedom. This solutions are obtained from solutions of systems of linear ordina
ry differential equations whose compatibility condition is the Garnier system. This solutions upto explicit transform also satisfy the Belavin --- Polyakov --- Zamolodchikov equations with four time variables and two space variables.
We find and study a two-parameter family of coupled Painleve II systems in dimension four with affine Weyl group symmetry of several types. Moreover, we find a three-parameter family of polynomial Hamiltonian systems in two variables $t,s$. Setting $
s=0$, we can obtain an autonomous version of the coupled Painleve II systems. We also show its symmetry and holomorphy conditions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
