The nonlinear Klein-Gordon equation and its application in modeling a nonlinear dispersive system
Thesis/Dissertation
·
OSTI ID:6964126
This thesis deals with the nonlinear Klein-Gordon (NKG) equation and one of its applications. Existing literature on the so-called NKG family and other NKG-type equations are first discussed, including interrelations, wherever possible, and existing particular solutions. Essential steps in the construction of particular solutions of some of thee equations are, thereafter, presented. The NKG equation without dispersion, and with quadratic and cubic nonlinearities, is then examined in greater detail, and periodic and aperiodic (algebraic) solitary-wave solutions are derived. Interactions between solitary-wave solutions of the NKG equation (with and without dispersion) and for baseband and envelope propagation, are numerically studied, and stabilization techniques are proposed. Finally, the NKG equation with cubic nonlinearity, and waveguide-type dispersion is used to rigorously analyze hysteresis and bistability during wave transmission through a linear nondispersive/nonlinear dispersive interface, to demonstrate an application of the NKG equation. Evidence of hysteresis in another physical system is also provided.
- Research Organization:
- Syracuse Univ., NY (USA)
- OSTI ID:
- 6964126
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
HYSTERESIS
KLEIN-GORDON EQUATION
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
STABILITY
WAVE EQUATIONS
WAVE PROPAGATION
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
HYSTERESIS
KLEIN-GORDON EQUATION
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
STABILITY
WAVE EQUATIONS
WAVE PROPAGATION