| Titre : | Behavior of the wave solutions under the effect of the nonlinearity |
| Titre original: | Comportements des solutions des ondes sous l’effet de la non linéarité |
| Auteurs : | Warda Djoudi , Auteur ; Abdelouahab Zerarka, Directeur de thèse |
| Type de document : | Thése doctorat |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2018 |
| Format : | 1 vol. (203 p.) |
| Langues: | Anglais |
| Mots-clés: | Equations non-linéaires,principe de l'équilibre homogène,méthodes des transformations fractionnelles,méthode de la variable fonctionnelle. |
| Résumé : |
This work aims to determine the behavior of wave solution under the effect of nonlinearity with the contribution of the homogeneous balance principle and analysis methods. In the first step we studied the nonlinear atomic lattice equation via the coth and coth-csch methods. Eight new travelling wave solutions have been obtained. In the same context, the method of fractional transformations is introduced and which has provided various exact solutions. In the second step we applied the functional variable method to a set of nonlinear BBM equations of constant coefficients and the general equation Kdv-mKdv of variable coefficients. |
| Sommaire : |
List of figures General introduction...........................................................1 Chapter 1 Some methods to solve the lattice differential equation ........ 4 1.1 Introduction ....................................................................... 4 1.2 The nonlinear lattice differential-difference equations (NDDEs) .... 4 1.2.1 A new expanded method for solving nonlinear differential-difference equation ................................................................................... 6 1.2.2 The non-linear lattice equation ...................................................... 8 1.3 Discussion and conclusion .................................................. 20 References ............................................................................ 22 Chapter 2 Exact fractional solutions of nonlinear lattice equation via some fractional transformation methods ............................. 29 2.1 Introduction ..................................................................... 29 2.2 Applications ...................................................................... 31 2.3 The fractional transformation methods ................................... 32 2.4 Discussion and conclusion .................................................. 47 References ............................................................................ 49 Chapter 3 Symbolic computational of nonlinear wave equation with constant coefficients via the functional variable method ......... 51 3.1 Introduction ...................................................................... 51 iv 3.2 Formulation of the method .................................................. 51 3.3 Application ...................................................................... 53 3.3.1 Benjamin-Bona-Mahony (BBM) equation .......................................... 54 3.3.2 Equation Benjamin-Bona-Mahony (BBM) with negative exponents ............ 60 3.3.3 A generalized form of the BBM equation ........................................... 66 3.3.4 A generalized form of the BBM equation with negative exponents ...... 69 3.4 Discussions ..................................................................... 75 3.5 Conclusion ...................................................................... 75 References ............................................................................ 77 Chapter 4 Exact solutions for the KdV-mKdV equation with timedependent coefficients using the modified functional variable method ................................................................................ 81 4.1 Introduction ...................................................................... 81 4.2 Description of the method fvm ............................................ 82 4.3 KdV-mKdV solutions ......................................................... 84 4.4 Partial structures .............................................................. 85 4.5 Full structures ................................................................. 86 4.6 Conclusion ....................................................................... 91 References ............................................................................ 93 General conclusion………………….…………..……………………………96 |
| En ligne : | http://thesis.univ-biskra.dz/3660/1/djoudi%20Thesis.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TPHY/58 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
