Mathematical physics is a discipline which combines both mathematics and physics. It could be understood as a the development of mathematical tools or methods in order to apply them to solve problems in physics and propose theories in physics. It is also understood as the use of mathematical methods for applications to problems appearing in physics. This is a very active research field split in many sub-fields.
In our group, we use mathematical methods developed in the last decades to solve nonlinear partial differential equations modelling the evolution of a wide range of phenomena. We are especially interested but not limited to the quest of solitary waves (topological excitations which appear in nonlinear media due a balance between dispersion and nonlinearity), periodic waves, vortices just to name a few. The properties of the nonlinear structures unveiled are elucidated and their relations of to experimental parameters are presented while possible experimental realizations are discussed. Our work finds applications to many physical fields where nonlinear waves are prominent objects such as wave propagation in photonic crystals, fiber optics and fluids.
Currently, we are seeking solitary waves solutions of the Kuramoto-Sivashinsky equation on the one hand and that of the Camassa-Holm equation on the second hand.
- H. M. Omanda, G. N’tchayi Mbourou, C. T. Djeumen Tchaho, and J. R. Bogning, KINK-BRIGHT SOLITARY WAVE SOLUTIONS OF THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION, Far East J. Dynam. Syst. 33, 59 (2021), http://dx.doi.org/10.17654/DS033010059
- C. T. Djeumen Tchaho, H. M. Omanda, G. N’tchayi Mbourou, J. R. Bogning, T. C. Kofané, Higher Order Solitary Wave Solutions of the Standard KdV Equations, Open Journal of Applied Sciences, 11, 103 (2021), https://doi.org/10.4236/ojapps.2021.111008
- C. T. Djeumen Tchaho, H. M. Omanda, G. N’tchayi Mbourou, J. R. Bogning, T. C. Kofané, Hybrid Dispersive Optical Solitons in Nonlinear Cubic-Quintic-Septic Schrödinger Equation, Optics and Photonics Journal 11, 23 (2021), https://www.scirp.org/journal/opj
- C. T. Djeumen Tchaho, H. M. Omanda, G. N’tchayi Mbourou, J. R. Bogning and T. C. Kofané, Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation, J. Phys. Commun. 3, 105013 (2019), https://doi.org/10.1088/2399-6528/ab4ba1
- C. T. Djeumen Tchaho, H. M. Omanda, and D. Belobo Belobo, Hybrid solitary waves for the generalized Kuramoto-Sivashinsky equation, Eur. Phys. J. Plus 133, 387 (2018), https://link.springer.com/article/10.1140%2Fepjp%2Fi2018-12218-4