Διανύουμε μια εποχή, όπου οι ανάγκες για μετάδοση πληροφορίας αυξάνονται ταχύτατα, με αποτέλεσμα τα χάλκινα καλώδια να μην αρκούν για να μεταδώσουν το πλήθος αυτό της πληροφορίας. Έτσι, περάσαμε στις Οπτικές Τηλεπικοινωνίες, όπου τα χάλκινα καλώδια αντικαταστάθηκαν από οπτικές ίνες και φορείς μετάδοσης της πληροφορίας δεν είναι πλέον τα ηλεκτρόνια αλλά τα φωτόνια. Κατά τη μετάδοση της πληροφορίας υπάρχουν όμως, φαινόμενα εξασθένησης και παραμόρφωσης του σήματος. Τη λύση σε αυτά τα προβλήματα καλείται να δώσει η χρήση σολιτονίων. Στην παρούσα διπλωματική εργασία, θα μελετήσουμε τον τρόπο με τον οποίον επηρεάζουν τα φαινόμενα ανώτερης τάξης την αλληλεπίδραση δύο γειτονικών σολιτονιακών παλμών που διαδίδονται μέσα σε μία οπτική ίνα. Πιο συγκεκριμένα, με τη χρήση αλγόριθμου της Fortran θεωρήσαμε δύο θεμελιώδεις σολιτονιακούς παλμούς και μελετήσαμε πως επηρεάζεται η διάδοσή τους κατά μήκος μιας οπτικής ίνας, αλλά και η μεταξύ τους αλληλεπίδρασή, από τη μεταξύ τους απόσταση, το σχετικό τους πλάτος καθώς και από τη διαφορά φάσης. Επιπλέον περιορίζοντας τη μεταξύ τους αλληλεπίδραση μελετήσαμε το πώς επηρεάζουν τη διάδοσή τους φαινόμενα ανώτερης τάξης όπως η σκέδαση Raman, η αυτό-διαμόρφωση απότομων άκρων (self-steepening) και η διασπορά τρίτης τάξης. / We are in an era where the need to transmit information rapidly increases, making the copper wires not enough to convey the multitude of this information. Thus, we moved on Optical Communications, where the copper cables were replaced by optical fibers and broadcasters of information are no longer electrons but photons. During the transmission of information we come across with problems such as attenuation and signal distortion. The use of solitons has come to give the solution to these problems. In this paper, we studied how the higher order phenomena, affects the interaction of two neighboring soliton pulses propagating through an optical fiber. More specifically, using a Fortran algorithm considering two fundamental soliton pulses we have studied how the propagation and their interaction is affected by their relative amplitude and phase difference. Also limiting the interaction between them, we have studied how the propagation is affected by higher order phenomena such as Stimulated Raman Scattering, Self Steepening and third order dispersion.

This research investigates wave propagation in an elastic half-space with a quadratic nonlinearity in its stress-strain relationship. Different boundary conditions on the surface are considered that result in both one- and two-dimensional wave propagation problems. The goal of the research is to examine the generation of second-order frequency effects and static effects which may be used to determine the nonlinearity present in the material. This is accomplished by extracting the amplitudes of those effects in the frequency domain and analyzing their dependency on the third-order elastic constants (TOEC). For the one-dimensional problems, both analytical approximate solutions as well as numerical simulations are presented. For the two-dimensional problems, numerical solutions are presented whose dependency on the material's nonlinearity is compared to the one-dimensional problems. The numerical solutions are obtained by first formulating the problem as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. In the one-dimensional cases, it is shown that the analytical and numerical solutions are in good agreement with each other, as well as how different boundary conditions may be used to measure the TOEC. In the two-dimensional cases, it is shown that there exist comparable dependencies of the second-order frequency effects and static effects on the TOEC. Finally, it is analytically and numerically investigated how multiple reflections in a plate can be used to simplify measurements of the material nonlinearity in an experiment.