| Title |
Antros eilės solitoninių sprendinių egzistavimas multiplikatyviuoju sąryšiu susietose Rikati lygtyse / |
| Translation of Title |
Existence of second order solitary solutions to Riccati differential equations coupled with a multiplicative term. |
| Authors |
Telksnys, Tadas |
| Full Text |
|
| Pages |
64 |
| Keywords [eng] |
differential equations ; multiplicative coupling ; inverse balancing ; operator method ; exact solution |
| Abstract [eng] |
Necessary and sufficient conditions for the existence of second order solitary solutions to Riccati equations coupled with multiplicative terms are derived in this thesis. Necessary conditions are obtained using the inverse balancing method, which generates the system parameters when the solution parameters are known. Sufficient conditions are derived using the generalized differential operator method. By utilizing the theory of linear recurring sequences the functional relationship between the solution parameters and initial conditions is obtained. It is demonstrated that when the parameters of the Riccati system satisfy the existence conditions for the second order solitary solution, all nonspecial solutions of the system are second order solitary solutions. The phase trajectories of these solutions are conic sections. The dynamical properties of the Riccati system are illustrated using computational examples. The computer algebra system Maple is used to derive the symbolic results of the thesis. |
| Dissertation Institution |
Kauno technologijos universitetas. |
| Type |
Master thesis |
| Language |
Lithuanian |
| Publication date |
2015 |
