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Exact solutions of non-linear Klein–Gordon equation with non-constant coefficients through the trial equation method
- Source :
- Journal of Mathematical Chemistry. 59:827-839
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- In this note, we use an extension of the trial equation method (also called the direct integral method) for partial differential equations with non-constant coefficients to derive exact solutions in the form of nonlinear waves. The model considered generalizes other classical models from physics like the Klein–Gordon equation, the $$(1 + 1)$$ -dimensional $$\phi ^4$$ -theory, the Fisher–Kolmogorov equation from population dynamics, and the Hodgkin–Huxley model which describes the propagation of electrical signals through the nervous system. As a particular example, the cylindrically symmetric cubic nonlinear Klein–Gordon equation is considered herein.
- Subjects :
- Physics
education.field_of_study
Constant coefficients
Partial differential equation
010304 chemical physics
Applied Mathematics
010102 general mathematics
Population
Mathematical analysis
Dynamics (mechanics)
General Chemistry
Extension (predicate logic)
01 natural sciences
symbols.namesake
Nonlinear system
0103 physical sciences
symbols
Direct integral
0101 mathematics
education
Klein–Gordon equation
Subjects
Details
- ISSN :
- 15728897 and 02599791
- Volume :
- 59
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Chemistry
- Accession number :
- edsair.doi...........43cf80c0181f5fdcabc3f2ef9ec35cd0