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Dispersion relation of the nonlinear Klein-Gordon equation through a variational method.
1Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, México. paolo@ucol.mx
Chaos (Woodbury, N.Y.)
|April 8, 2006
Summary
This study presents analytical approximations for the nonlinear Klein-Gordon equation
Area of Science:
- Theoretical Physics
- Nonlinear Dynamics
- Quantum Field Theory
Background:
- The nonlinear Klein-Gordon equation is a fundamental model in physics.
- Strong nonlinearities pose significant challenges for analytical solutions.
- Existing methods often rely on numerical simulations or complex functions.
Purpose of the Study:
- To develop a novel analytical method for approximating the dispersion relation.
- To handle strong nonlinearities in the Klein-Gordon equation effectively.
- To provide accurate and systematically improvable approximations.
Main Methods:
- Application of the linear delta expansion method.
- Derivation of fully analytical expressions.
- Avoidance of special functions.
Main Results:
- Approximate expressions for the dispersion relation were derived.
- The method successfully addresses strong nonlinearities.
- Results demonstrate systematic approximation capabilities.
Conclusions:
- The linear delta expansion offers a powerful and simpler approach.
- The derived expressions provide accurate and systematic approximations.
- This method yields superior and more accessible results compared to existing literature.
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