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3. Introduction

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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4. Linear Bundles of Lie Algebras and Compatible Poisson Structures

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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5. The Inverse Scattering Problem for the Zakharov–Shabat System

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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6. The NLEEs and the Gauge Transformations

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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7. Poisson–Nijenhuis structures Related to the Generalized Zakharov–Shabat System

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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8. Integrability and Nijenhuis Tensors

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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9. Vector-Valued Differential Forms

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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10. Smooth Manifolds

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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11. Hamiltonian Dynamics

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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12. The Classical r-Matrix Method

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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13. Fundamental Properties of the solvable NLEEs

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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14. Hierarchies of Hamiltonian structures

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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15. The Generalized Fourier Transforms

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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16. The Direct Scattering Problem for theZakharov–Shabat System

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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17. The Lax Representation and the AKNS Approach

Author

Gerdjikov, V.S., Vilasi, G., Yanovski, A.B., Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Gerdjikov, V.S., editor, Vilasi, G., editor, and Yanovski, A.B., editor

Published
2008
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29. Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type

Author

Gerdjikov, V.S. and Kostov, N.A.

Subjects
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Abstract

New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of DIII-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov. The relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert problem. The minimal sets of scattering data Ti, i = 1, 2 which allow one to reconstruct uniquely both the scattering matrix and the potential of the Lax operator are defined. The effect of the new reductions on the hierarchy of Hamiltonian structures of MMKdV and on Ti are studied. We illustrate our results by the MMKdV equations related to the algebra g @ so(8) and derive several new MMKdV-type equations using group of reductions isomorphic to Z₂, Z₃, Z₄.

Published
2008

31. N-Wave Equations with Orthogonal Algebras: Z₂ and Z₂ × Z₂ Reductions and Soliton Solutions

Author

Gerdjikov, V.S., Kostov, N.A., and Valchev, T.I.

Subjects
Nonlinear Sciences::Exactly Solvable and Integrable Systems, Nonlinear Sciences::Pattern Formation and Solitons
Abstract

We consider N-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first Z₂-reduction is the canonical one. We impose a second Z₂-reduction and consider also the combined action of both reductions. For all three types of N-wave equations we construct the soliton solutions by appropriately modifying the Zakharov-Shabat dressing method. We also briefly discuss the different types of one-soliton solutions. Especially rich are the types of one-soliton solutions in the case when both reductions are applied. This is due to the fact that we have two different configurations of eigenvalues for the Lax operator L: doublets, which consist of pairs of purely imaginary eigenvalues, and quadruplets. Such situation is analogous to the one encountered in the sine-Gordon case, which allows two types of solitons: kinks and breathers. A new physical system, describing Stokes-anti Stokes Raman scattering is obtained. It is represented by a 4-wave equation related to the B₂ algebra with a canonical Z₂ reduction.

Published
2007

32. Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras

Author

Gerdjikov, V.S. and Grahovski, G.G.

Abstract

The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E₆ and E₇. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.

Published
2006

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