| Title |
Construction of solitary solutions to differential equations via operator techniques / |
| Translation of Title |
Solitoninių sprendinių diferencialinėms lygtims konstravimas taikant operatorinius metodus. |
| Authors |
Telksnys, Tadas |
| Full Text |
|
| Pages |
50 |
| Keywords [eng] |
soliton solution ; operator method ; differential equations |
| Abstract [eng] |
A novel mathematical and computational framework for the construction of solitary solutions to various types of nonlinear differential equations, including ordinary differential equations (ODE), partial differential equations (PDE), and fractional differential equations (FDE) is presented in this thesis. Solitary solutions have a plethora of unique physical and mathematical properties that influence the behavior of the considered system. The developed techniques are based on the application of symbolic computations to generalized differential operators. Such operators can be used to generate the coefficients of the series solution to differential equations, after which symbolic computations and linear recurring sequences are used to transform the series solution into the closed form solution. Necessary and sufficient conditions that differential equations must satisfy in order for the developed techniques to be applicable are discussed, as well the value of such techniques in applications. A real-world system of hepatitis C virus evolution is considered – it is shown that this system admits solitary solutions when the system parameters take biologically significant values. Fractional-order differential equations are also considered: it is demonstrated under what conditions these equations can be transformed into more complex ordinary differential equations and that the developed techniques can be used to construct solitary solutions. |
| Dissertation Institution |
Kauno technologijos universitetas. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2020 |
