Dimitri J. Frantzeskakis, G. Theocharis, F. K. Diakonos, Peter Schmelcher, and Yuri S. Kivshar Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece Theoretische Chemie, Physikalisch-Chemisches Institut, INF 229, 69120 Heidelberg, Germany Nonlinear Physics Group, Research School of Physical Sciences and Engineering, Australian National University, Canber...

Waleed H Omer ([email protected]) Akira Narita ([email protected]) Kazuyoshi Hosomichi ([email protected]) Shigeki Mitsunaga ([email protected]) Yasuhiro Hayashi ([email protected]) Atsushi Yamashita ([email protected]) Avdyl Krasniqi ([email protected]) Yuri Iwasaki ([email protected]) Masami Kimura ([email protected]) Ituro Inoue...

We use a new version of the Definability Theorem of Beth in order to unify classical Theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory. A.M.S. Classification: Primary 03B99; Secondary 11D99.

Yana V. Izdebskaya,* Anton S. Desyatnikov, Gaetano Assanto, and Yuri S. Kivshar Nonlinear Physics Center, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia Department of Physics, Taurida National University, Simferopol 95007, Ukraine Nonlinear Optics and OptoElectronics Lab, University of Rome “Roma Tre,” Rome 00146, Italy *Correspondin...

Michał Matuszewski, Wieslaw Krolikowski, and Yuri S. Kivshar Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia Laser Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia Received 29 September 2008; revised manuscript received 17 November 2008; publ...