Lax Pairs
On the origin of dual Lax pairs and their r-matrix structure
... We now apply our scheme to n = 2 and k = 4 . This gives rise to equations that generalize those studied in [14] which are related to a wealth of NLS-type equations: derivative NLS equation of the Kaup-Newell hierarchy ...
39
ΖN graded discrete Lax pairs and integrable difference equations
... spectral parameter. We give a classification scheme for such Lax pairs and the associated integrable lattice systems. We present two potential forms and completely classify the generic case. Many well known ...
31
Painlev´e Analysis, Lax Pairs and New Analytic Solutions for a High-order Boussinesq-Burgers Equation
... In this work, with symbolic computation, we have per- formed the Painlev´e analysis for Eq. (1), and Lax pairs be obtained following the AKNS procedure. We have given the auto-B¨acklund transformation via ...
5
ZN graded discrete Lax pairs and Yang-Baxter maps
... Lax pairs were defined for Yang-Baxter maps in [10, 9]. A matrix L(x, a), with x ∈ X, depending upon the YB parameter a and the spectral parameter λ is used to define the equation: L(x ′ , a)L(y ′ , b) = ...
15
On Lax pairs and matrix extended simple Toda systems
... characteristic curve, which confirms that there is not enough constants of motion found via the traces of powers of L to justify the complete integrability of this system. The cor- responding algebraic curve is closer to ...
13
Reductions of integrable equations: dihedral group
... A very important issue is the solution of nonlinear integrable models. The reduction group proves to be not only a very useful tool to find new integrable equations and classify Lax pairs but also a ...
18
Lax pair and super-Yangian symmetry of the nonlinear super-Schrodinger equation
... We consider a version of the nonlinear Schro¨dinger equation with M bosons and N fermions. We first solve the classical and quantum versions of this equation, using a super-Zamolodchikov–Faddeev 共 ZF 兲 algebra. Then we ...
28
Casimirs and Lax Operators from the Structure of Lie algebras
... Invariant functions generate invariant vectors, which offers a method of incorporating the conservation laws into the mathematical equations and enable systems in Geometric Control and Quantum control to be resolved. ...
17
Closed form solution for p-curves in SO(4)
... By using the symmetry of the 4D rotation group SO (4), it was possible to find a closed form solution to the fully assessable and controllable 6 dimensional problem. p-curves are interesting because, with just 3 input ...
7
Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation
... In this paper, we have introduced an integrable coupling of the known differential-difference equation, and presented its Lax pair. With the help of a gauge transformation of the corresponding Lax ...
7
Nonlinear Evolution Equations for Second-order Spectral Problem
... nonlinearized Lax pairs, Euler-Lagrange function and Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is ...the Lax pairs is equivalent to matrix spectral ...
8
Plant embryogenesis requires AUX/LAX mediated auxin influx
... The plant hormone auxin and its directional transport are known to play a crucial role in defining the embryonic axis and subsequent development of the body plan. Although the role of PIN auxin efflux transporters has ...
10
G(2)-Calogero-Moser Lax operators from reduction
... coupling constants depending on whether the potential involves roots which are mapped to long or short roots. This relation is dictated by the Lax pair construction, and coincides with the one found by Olshanetsky ...
13
Comparison of MOC and Lax FDE for simulating transients in Pipe Flows
... Now applying the developed numerical model using Lax FDE method to the hydraulic transient case discussed above the following results are obtained and plotted as shown graphically. In this case we have considered ...
5
Using LaX scintillator in a new low-background Compton telescope
... employing LaX scintillators for the calorimeter, one can take advantage of the unique speed and resolving power of the material to improve the instrument sensitivity and simultaneously enhance its spectroscopic ...
11
Broken promises: the politics of lax enforcement of tax laws in Egypt
... Microsoft Word PhD final corrected changes accepted copy docx 1 The London School of Economics and Political Science Broken Promises – The Politics of Lax Enforcement of Tax Laws in Egypt Moritz Schmo[.] ...
256
Plant embryogenesis requires AUX/LAX mediated auxin influx
... While testing the utility of Brassica napus microspore embryos as high throughput assay system, we uncovered an unexpected role for auxin influx during early embryo development - unexpected because auxin import during ...
32
Numerical analysis of stability for a nonlinear size-structured population model with elastic growth
... numerical methods solving size-structured models [14]: Lax-Wendroff scheme, Box method,.. and characteristic curves.[r] ...
15
EFFECT OF SECURITY RISK CONTROL PROGRAMMES ON SAFETY IN UNIVERSITIES IN THARAKA NITHI AND MERU COUNTIES
... ii.It was established that majority of the security risk control programmes were lax or not working effectively, Universities need to follow the guidelines by the America[r] ...
38
Quaternionic representation of the moving frame for surfaces in Euclidean three space and Lax pair
... Equations (2) for the moving frame are rewritten using the Lie algebra isomorphism between so(3) and so(2) in terms of 2 × 2 matrices. The quaternionic representation of surfaces permits the identification of the ...
8