1,911 research outputs found
On the remarkable relations among PDEs integrable by the inverse spectral transform method, by the method of characteristics and by the Hopf-Cole transformation
We establish deep and remarkable connections among partial differential
equations (PDEs) integrable by different methods: the inverse spectral
transform method, the method of characteristics and the Hopf-Cole
transformation. More concretely, 1) we show that the integrability properties
(Lax pair, infinitely-many commuting symmetries, large classes of analytic
solutions) of (2+1)-dimensional PDEs integrable by the Inverse Scattering
Transform method (-integrable) can be generated by the integrability
properties of the (1+1)-dimensional matrix B\"urgers hierarchy, integrable by
the matrix Hopf-Cole transformation (-integrable). 2) We show that the
integrability properties i) of -integrable PDEs in (1+1)-dimensions, ii) of
the multidimensional generalizations of the GL(M,\CC) self-dual Yang Mills
equations, and iii) of the multidimensional Calogero equations can be generated
by the integrability properties of a recently introduced multidimensional
matrix equation solvable by the method of characteristics. To establish the
above links, we consider a block Frobenius matrix reduction of the relevant
matrix fields, leading to integrable chains of matrix equations for the blocks
of such a Frobenius matrix, followed by a systematic elimination procedure of
some of these blocks. The construction of large classes of solutions of the
soliton equations from solutions of the matrix B\"urgers hierarchy turns out to
be intimately related to the construction of solutions in Sato theory. 3) We
finally show that suitable generalizations of the block Frobenius matrix
reduction of the matrix B\"urgers hierarchy generates PDEs exhibiting
integrability properties in common with both - and - integrable
equations.Comment: 30 page
Wanprestasi Pembayaran Klaim Asuransi Jiwa Akibat Kelalaian Penyerahan Berkas oleh Mitra Penanggung sebagai Kolektor Pengajuan Klaim (Studi Kasus Sertifikat Asuransi Polis Nomor 15.001673)
At this time many banks are incentive to lure consumer credit to consumers. In general, consumer loan interest rate is higher than productive credit, even there is a fixed rate. It seems that the fixed rate makes it easy to organize family finances, paying only monthly installments of the same amount, but if carefully calculated, the interest is much higher. Consumer Loan Protection with Insurance Policy Certificate 15.001673 is a life insurance product that guarantees repayment of the remaining amount of Loans and / or monthly loan installment of the Customer as Participant (Insured) to the Policyholder in case the Participant (the Insured) has a death risk or total temporary disability / Or total permanent disability. Although it is clear about the rights and obligations in the insurance agreement but the reality is very different because it turns out the insurer does not fulfill its obligations in the event of claim submission from the insured. Rejection of insurance claims may be made by the insurer under the pretext of submitting the file beyond the specified time limit. Issues to be studied further is how validation of denial of life insurance claim made by Jasindo in accordance with the insurance policy and existing legislation and whether Partner Error is can be classified as Wanprestasi payment of Insurance Claim for late in submission of policy file No: 15.001673. In conducting research, this research is normative law research that is research having object of study about rule or rule. The objective is to determine the validity of the refusal of insurance claims made by Jasindo in accordance with the existing insurance policies and regulations and to find out the Default Payment of Insurance Claims due to Delayed Submission by Marketing Party as Collector Submission of Claim on Insurance Certificate Number 15.00167
Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
An integrable self-adjoint 7-point scheme on the triangular lattice and an
integrable self-adjoint scheme on the honeycomb lattice are studied using the
sublattice approach. The star-triangle relation between these systems is
introduced, and the Darboux transformations for both linear problems from the
Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A
geometric interpretation of the Laplace transformations of the self-adjoint
7-point scheme is given and the corresponding novel integrable discrete 3D
system is constructed.Comment: 15 pages, 6 figures; references added, some typos correcte
Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions
In this paper we develop a dressing method for constructing and solving some
classes of matrix quasi-linear Partial Differential Equations (PDEs) in
arbitrary dimensions. This method is based on a homogeneous integral equation
with a nontrivial kernel, which allows one to reduce the nonlinear PDEs to
systems of non-differential (algebraic or transcendental) equations for the
unknown fields. In the simplest examples, the above dressing scheme captures
matrix equations integrated by the characteristics method and nonlinear PDEs
associated with matrix Hopf-Cole transformations.Comment: 31 page
Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation
We apply a version of the dressing method to a system of four dimensional
nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer
equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform
Method) and nonlinear matrix PDE integrable by the method of characteristics as
particular reductions. Some other reductions are suggested.Comment: 12 page
Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I
We propose an algorithmic procedure i) to study the ``distance'' between an
integrable PDE and any discretization of it, in the small lattice spacing
epsilon regime, and, at the same time, ii) to test the (asymptotic)
integrability properties of such discretization. This method should provide, in
particular, useful and concrete informations on how good is any numerical
scheme used to integrate a given integrable PDE. The procedure, illustrated on
a fairly general 10-parameter family of discretizations of the nonlinear
Schroedinger equation, consists of the following three steps: i) the
construction of the continuous multiscale expansion of a generic solution of
the discrete system at all orders in epsilon, following the Degasperis -
Manakov - Santini procedure; ii) the application, to such expansion, of the
Degasperis - Procesi (DP) integrability test, to test the asymptotic
integrability properties of the discrete system and its ``distance'' from its
continuous limit; iii) the use of the main output of the DP test to construct
infinitely many approximate symmetries and constants of motion of the discrete
system, through novel and simple formulas.Comment: 34 pages, no figur
An integrable generalization of the Toda law to the square lattice
We generalize the Toda lattice (or Toda chain) equation to the square
lattice; i.e., we construct an integrable nonlinear equation, for a scalar
field taking values on the square lattice and depending on a continuous (time)
variable, characterized by an exponential law of interaction in both discrete
directions of the square lattice. We construct the Darboux-Backlund
transformations for such lattice, and the corresponding formulas describing
their superposition. We finally use these Darboux-Backlund transformations to
generate examples of explicit solutions of exponential and rational type. The
exponential solutions describe the evolution of one and two smooth
two-dimensional shock waves on the square lattice.Comment: 14 pages, 4 figures, to appear in Phys. Rev. E http://pre.aps.org
- …