Exact Travelling Wave Solution of Some Nonlinear Partial Differential Equations
| dc.contributor.author | Lal, Bhajan | |
| dc.contributor.supervisor | Gupta, Rajesh Kumar | |
| dc.date.accessioned | 2011-12-12T06:54:11Z | |
| dc.date.available | 2011-12-12T06:54:11Z | |
| dc.date.issued | 2011-09-12 | |
| dc.description | M.Sc. (Mathematics and Computing) | en |
| dc.description.abstract | Exact solutions to nonlinear partial differential equations play an important role for understanding of qualitative as well as quantitative features of many phenomena and processes. Exact solutions visually demonstrate and make it possible to understand the mechanism of complex nonlinear effects. The thesis entitled “Exact Travelling Wave Solutions of Some Nonlinear Partial Differential Equations” is an attempt to obtain the exact solutions of some nonlinear partial differential equations. The thesis has been divided into six chapters. The brief outline of the research work presented chapter wise in the thesis is as follows: First chapter is introductory in nature, in this chapter, definition of nonlinear differential equations and basic concepts are discussed. A brief summary of literature available on the subject and summary of the work presented in the thesis also appears in this chapter. In the second chapter, methodology of ÷ ø ö ç è æ G G' -expansion method and modified ÷ø ö ç è æ G G' -expansion method have been presented. In the third chapter, sinh-Gordon equation has been solved by using ÷ ø ö ç è æ G G' - expansion method. We have successfully derived two type of travelling wave solution in term of hyperbola and trigonometric functions for the generalized sinh-Gorden equation by using the ÷ ø ö ç è æ G G' -expansion method. The fourth chapter comprises Huber’s equation with solved by ÷ ø ö ç è æ G G' -expansion method and in fifth chapter we have obtained exact travelling wave solution of ZK-BBM equation by ÷ ø ö ç è æ G G' -expansion method. In the sixth chapter Boussinesq equation has been solved with the modified ÷ ø ö ç è æ G G' - expansion method. We have successfully derived travelling wave solution in term of trigonometric functions for the generalized Boussinesq equation by using the modified ÷ø ö ç è æ G G' -expansion method. It is worth to mention that all the solutions reported in this thesis are new and authenticity of the solutions is checked by Maple software. | en |
| dc.format.extent | 969860 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/10266/1597 | |
| dc.language.iso | en | en |
| dc.subject | Partial Differential Equations | en |
| dc.subject | Exact Solutions | en |
| dc.subject | (G'/G)-Expansion Method | en |
| dc.title | Exact Travelling Wave Solution of Some Nonlinear Partial Differential Equations | en |
| dc.type | Thesis | en |