We want to classify local Poisson brackets w. The study of bihamiltonian structures was initiated by F. Magri [38] in his analysis of the so-called Lenard scheme of constructing the KdV integrals. Dorfman and I.

Fokas and B. Fuchssteiner [22] discovered the connections between the bihamiltonian scheme and the theory of hereditary symmetries of integrable equations. However, it is not easy to appl Documents: Advanced Search Include Citations. Hamiltonian operators and algebraic structures related to them, by Dorfman.

Venue: Funct. Add To MetaCart. Our aim is to embed the theory of Gromov- Witten invariants of all genera into the theory of integrable systems. The project is focused at describing normal forms of the PDEs and their The project is focused at describing normal forms of the PDEs and their local bihamiltonian structures satisfying certain simple axioms. A Frobenius manifold or its degeneration is associated to every bihamiltonian structure of our type.

The main result is a universal loop equation on the jet space of a semisimple Frobenius manifold that can be used for perturbative reconstruction of the integrable hierarchy. We show that first few terms of the perturbative expansion correctly reproduce the universal identities between intersection numbers of Gromov- Witten classes and their descendents. Citation Context Poisson cohomology and quantization by Johannes Huebschmann - J. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the pert Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives.

The main tools is in constructing of the so-called quasi-Miura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bihamiltonian structure of hydrodynamic type the quasitriviality theorem. We also describe, following [35], the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending. The problem of integrable discretization: Hamiltonian approach by Yuri B.

**N2--Solve Basic Linear Diophantine Equation**

Suris - Progress in Mathematics, Volume Rok Baran, P. Blaschke, M. Marvan and I. Krasil'shchik, On symmetries of the Gibbons-Tsarev equation. Journal of Geometry and Physics Cavro, Recurrence in non-autonomous dynamical systems. Journal of Difference Equations and Applications 25 No. Complex Variables and Elliptic Equations 64 No. Bommier-Hato and E-H. Youssfi, Radial balanced metrics on the unit ball of the Kepler manifold.

Journal of Mathematical Analysis and Applications No. Upmeier, Reproducing kernel functions and asymptotic expansions on Jordan-Kepler manifolds. Advances in MathematicsM. Ergodic Theory and Dynamical Systems 39 No. Eleuteri, E. Ipocoana and P. Extended Abstracts Spring Roth, Constant slope models and perturbation. Israel Journal of Mathematics No. Marvan and M. Pavlov, Integrable dispersive chains and their multi-phase solutions, Letters in Mathematical Physicsâ€” Qualitative Theory of Dynamical Systems 18 No.

Pravec, Remarks on definitions of periodic points for nonautonomous dynamical system. Roth and J. Bobok, The infimum of Lipschitz constants in the conjugacy class of an interval map.

Proceedings of the American Mathematical Society No. Sergyeyev and I.

Applied Mathematics Letters 92 Sergyeyev, S. Skurativskyi and V. Vladimirov, Compacton solutions and non integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules.We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem.

Click on title above or here to access this collection. An asymptotic equation for weakly nonlinear hyperbolic waves governed by variational principles is derived and analyzed. The equation is used to study a nonlinear instability in the director field of a nematic liquid crystal. It is shown that smooth solutions of the asymptotic equation break down in finite time.

Also constructed are weak solutions of the equation that are continuous despite the fact that their spatial derivative blows up. Sign in Help View Cart. Article Tools. Add to my favorites. Recommend to Library. Email to a friend. Digg This. Notify Me! E-mail Alerts. RSS Feeds. SIAM J. Related Databases. Web of Science You must be logged in with an active subscription to view this. Keywords nonlinear hyperbolic partial differential equationsliquid crystalsgeometrical optics.

Publication Data. Publisher: Society for Industrial and Applied Mathematics. John K. Hunter and Ralph Saxton. Cited by Singularity and existence for a multidimensional variational wave equation arising from nematic liquid crystals.

Journal of Mathematical Analysis and Applications :2, Journal of Mathematical Fluid Mechanics 22 Theoretical and Mathematical Physics :2, The purpose of this present article is to study the modified Veronese web mVw equation and to obtain its infinitesimals, commutation table of Lie algebra, symmetry reductions and closed form analytical solutions. The solutions are analysed physically via numerical simulation. Consequently, elastic behaviour multisolitons, line soliton, doubly soliton, parabolic wave profile, nonlinear behaviour of wave profile and elastic interaction soliton profile of solutions are demonstrated in the analysis and discussion section to make this study more praiseworthy.

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## SIAM Journal on Applied Mathematics

Rent this article via DeepDyve. Qiu, J. IEEE Trans. Fuzzy Syst. Google Scholar. Sun, K. Wazwaz, A. Nonlinear Dyn. Xu, G. Ferapontov, E. Zakharevich, I. Dunajski, M. SI] Lelito, A. Boris, K. Marvan, M. In: Proceedings Conference, Brno, pp.Cen, J. Nonlinear classical and quantum integrable systems with PT -symmetries. Unpublished Doctoral thesis, City, University of London.

A key feature of integrable systems is that they can be solved to obtain exact analytical solutions. In this thesis we show how new models can be found through generalisations of some well known nonlinear partial differential equations including the Korteweg-de Vries, modified Korteweg-de Vries, sine-Gordon, Hirota, Heisenberg and Landau-Lifschitz types with joint parity and time symmetries whilst preserving integrability properties.

The first joint parity and time symmetric generalizations we take are extensions to the complex and multicomplex fields, such as bicomplex, quaternionic, coquaternionic and octonionic types. Moreover, in agreement with the reality property present in joint parity and time symmetric non-Hermitian quantum systems, we find joint parity and time symmetries also play a key role for reality of conserved charges for the new systems, even though the soliton solutions are complex or multicomplex.

Our complex extensions have proved to be successful in helping one to obtain regularized degenerate multi-soliton solutions for the Korteweg-de Vries equation, which has not been realised before.

We extend our investigations to explore degenerate multi-soliton solutions for the sine-Gordon equation and Hirota equation. In particular, we find the usual time-delays from degenerate soliton solution scattering are time-dependent, unlike the non-degenerate multi-soliton solutions, and provide a universal formula to compute the exact time-delay values for scattering of N-soliton solutions.

Whilst developing new methods for the construction of soliton solutions for these systems, we xiv find new types of solutions with different parameter dependence and qualitative behaviour even in the one-soliton solution cases. We exploit gauge equivalence between the Hirota system with continuous Heisenberg and Landau-Lifschitz systems to see how nonlocality is inherited from one system to another and vice versa. In the final part of the thesis, we extend some of our investigations to the quantum regime.

In particularwe generalize the scheme of Darboux transformations for fully timedependent non-Hermitian quantum systems, which allows us to create an infinite tower of solvable models. Library Services. Unpublished Doctoral thesis, City, University of London Abstract A key feature of integrable systems is that they can be solved to obtain exact analytical solutions. Downloads per month over past year.Read this paper on arXiv.

These results were recently applied by I. Krichever and B.

### Volume 196, Issue 2, August 2018

Dubrovin to prove integrability of some models in topological field theories. Within the geometric framework we derive some new integrable in a sense to be discussed generalizations describing N -wave resonant interactions.

Ten years ago [10] a natural hamiltonian formalism was proposed for the class of homogeneous systems of PDE. Later see [11] it was generalized for the class of multidimensional. As we have proved in [32], these properties hamiltonian property and diagonalizability imply integrability.

Deeper insight into this type of integrability is given by the theory of orthogonal curvilinear coordinate systems. This chapter of classical differential geometry was being intensively developed at the beginning of the XX century [6], [8], [20].

These forgotten corners of differential geometry seem to be worth revisiting. An example. Diagonal systems of hydrodynamic type and orthogonal curvilinear coordinate systems in R n. Let us recall briefly the main results of [10],[32]. Dubrovin and S. Lemma [32], [33]. From a differential geometric point of view, to give a zero curvature nondegenerate diagonal metric is equivalent to giving an orthogonal curvilinear coordinate system on a flat possibly pseudo-Euclidean space see [6].

A striking fact can be discovered: formula 3 was found in [6] p. One can prove [33] the completeness property for this class of symmetries and solutions parameterized by n functions of 1 variable - the generic Cauchy data for our diagonal system 1.

### Volume 196, Issue 2, August 2018

The corresponding geometric notion used in the theory of orthogonal curvilinear coordinate systems corresponding to 3 is the so called Combescure transformation see [6]. The theory of Combescure transformations coincides with the theory of integrable diagonal systems of hydrodynamic type. As we have demonstrated earlier [34] this is a consequence of Galilei invariance of the original systems.Structure of the Institute Departments Institute.

Conditions and Application Conditions for the admission Electronic application form. Study Seminars Ph. Defences Information System SU. Publishing Activity Scientific journals Publications. Year Complex Variables and Elliptic Equations 64 No. Marvan and M. Pavlov, Integrable dispersive chains and their multi-phase solutions, Letters in Mathematical Physicsâ€” Roth and J.

Bobok, The infimum of Lipschitz constants in the conjugacy class of an interval map. Proceedings of the American Mathematical Society No. Balibrea, J. Baran, I. Krasil'shchik, O. Morozov, P. Eleuteri, J. Raith, Stability of the distribution function for piecewise monotonic maps on the interval, Discrete and Continuous Dynamical Systems - Series A 38â€” Misiurewicz and S. Holba, I. Block, J. Keesling, L. Makka, K. Hofreiter, K. Pavlov, A new class of solutions for the multi-component extended Harry Dym equation, Wave Motion 74 Sergyeyev, A simple construction of recursion operators for multidimensional dispersionless integrable systems, Journal of Mathematical Analysis and Applications Blaschke, Z.

Blaschke and P. Blaschke, Classical corrections to black hole entropy in d dimensions: A rear window to quantum gravity? Blaszak and A.

Oprocha and M. Chudziak and Z. Opanasenko, A. Bihlo and R. Chowdhury, S. Ali and M. Marvan and A.

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