اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدComplete point-symmetry group, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
116
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We carry out extended symmetry analysis of the (1+2)-dimensional Boiti-Leon-Pempinelli system, which enhances and generalizes many results existing in the literature. The complete point-symmetry group of this system is computed using an original megaideal-based version of the algebraic method. A number of meticulously selected differential constraints allow us to construct families of exact solutions of this system, which are significantly larger than all known ones. After classifying one- and two-dimensional subalgebras of the entire (infinite-dimensional) maximal Lie invariance algebra of this system, we study only its essential Lie reductions, which give solutions beyond the above solution families. Among reductions of the Boiti-Leon-Pempinelli system via differential constraints or Lie symmetries, we identify a number of famous partial and ordinary differential equations. We also show how all the constructed solution families can significantly be extended using Laplace and Darboux transformations.
قيم البحث
اقرأ أيضاً
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example t
o illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.
A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and nonclassical symmetry points of view. The classifications of Lie reduction operators and of regular no
nclassical reduction operators are performed. The set of admissible transformations (the equivalence groupoid) of the class is described exhaustively. The criterion of reducibility of variable coefficient Newell-Whitehead-Segel equations to their constant coefficient counterparts is derived. Wide families of exact solutions for such variable coefficient equations are constructed.
The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordin
ates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.
Essentially generalizing Lies results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-order prolongation of its point equivalence groupoid, and then we carry ou
t the complete group classification of this class. Since it is normalized, the algebraic method of group classification is naturally applied here. Using the specific structure of the equivalence group of the class, we essentially employ the classical Lie theorem on realizations of Lie algebras by vector fields on the line. This approach allows us to enhance previous results on Lie symmetries of equations from the class and substantially simplify the proof. After finding a number of integer characteristics of cases of Lie-symmetry extensions that are invariant under action of the equivalence group of the class under study, we exhaustively describe successive Lie-symmetry extensions within this class.
The Theory of (2+1) Systems based on 2D Schrodinger Operator was started by S.Manakov, B.Dubrovin, I.Krichever and S.Novikov in 1976. The Analog of Lax Pairs introduced by Manakov, has a form $L_t=[L,H]-fL$ (The $L,H,f$-triples) where $L=partial_xpar
tial_y+Gpartial_y+S$ and $H,f$-some linear PDEs. Their Algebro-Geometric Solutions and therefore the full higher order hierarchies were constructed by B.Dubrovin, I.Krichever and S.Novikov. The Theory of 2D Inverse Spectral Problems for the Elliptic Operator $L$ with $x,y$ replaced by $z,bar{z}$, was started by B.Dubrovin, I.Krichever and S.Novikov: The Inverse Spectral Problem Data are taken from the complex Fermi-Curve consisting of all Bloch-Floquet Eigenfunctions $Lpsi=const$. Many interesting systems were found later. However, specific properties of the very first system, offered by Manakov for the verification of new method only, were not studied more than 10 years until B.Konopelchenko found in 1988 analogs of Backund Transformations for it. He pointed out on the Burgers-Type Reduction. Indeed, the present authors quite recently found very interesting extensions, reductions and applications of that system both in the theory of nonlinear evolution systems (The Self-Adjoint and 2D Burgers Hierarhies were invented, and corresponding reductions of Inverse Problem Data found) and in the Spectral Theory of Important Physical Operators (The Purely Magnetic 2D Pauli Operators). We call this system GKMMN by the names of authors who studied it.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
