ANALYSIS OF SOLITON RESONANCE BY USING FULLY-NONLINEAR AND STRONGLY-DISPERSIVE WAVE MODEL

Soliton-complex Dynamics in Strongly Dispersive Medium

The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its ”excited” states are described analytically and numerica...

Slow Passage through Resonance for a Weakly Nonlinear Dispersive Wave

Local and global analysis of nonlinear dispersive and wave equations

Contents Preface ix Chapter 1. Ordinary differential equations 1 1.1. General theory 1 1.2. Gronwall's inequality 7 1.3. Bootstrap and continuity arguments 14 1.4. Noether's theorem 18 1.5. Monotonicity formulae 25 1.6. Linear and semilinear equations 28 1.7. Completely integrable systems 35 Chapter 2. Constant coefficient linear dispersive equations 41 2.1. The Fourier transform 47 2.2. Fundam...

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

Interaction of an optical soliton with a dispersive wave.

Scattering of a dispersive wave by optical solitons is studied experimentally in photonic crystal fibers in cases when the soliton and the dispersive wave have either identical or orthogonal polarization states. Observations of new resonant frequencies are reported. The experimental results are compared to numerical simulations and predictions from the recently derived wave vector matching cond...