Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network
We investigate the propagation of modulated solitons in a two-dimensional (2D) nonlinear reaction diffusion electrical network with the intersite circuit elements (both in the propagation and transverse directions) acting as nonlinear resistances. Model equations for the circuit are derived and they...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-07-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S221137972300325X |
| _version_ | 1797802229174894592 |
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| author | Joel Bruno Gonpe Tafo Fabien Kenmogne Alexandre Mando Kongne Roger Eno David Yemélé |
| author_facet | Joel Bruno Gonpe Tafo Fabien Kenmogne Alexandre Mando Kongne Roger Eno David Yemélé |
| author_sort | Joel Bruno Gonpe Tafo |
| collection | DOAJ |
| description | We investigate the propagation of modulated solitons in a two-dimensional (2D) nonlinear reaction diffusion electrical network with the intersite circuit elements (both in the propagation and transverse directions) acting as nonlinear resistances. Model equations for the circuit are derived and they reduce from the reductive perturbation technique to the 2D nonlinear dissipative Schrödinger equation governing the propagation of the small dissipative amplitude signals in the network. This equation does’nt have conserved quantities and it admits as solutions the 2D dissipative pulse and dark solitons, according to the sign of the product of dispersive and nonlinearity coefficients, with amplitude which narrows as the time increases. The exactness of the analytical analysis is confirmed by numerical simulations. Then by using the method of constants variation, the train of periodic pulse and dark solitons are also found, with their existence constraints also connected to the sign of the product of dispersive and nonlinearity coefficients, as found for standard pulse and dark solitons. Then the modulational instability (MI) criterion in system is found and is connected to the existence of modulated solitons. |
| first_indexed | 2024-03-13T05:02:54Z |
| format | Article |
| id | doaj.art-383f478da8fd4f76af58be56af3f50ba |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-13T05:02:54Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-383f478da8fd4f76af58be56af3f50ba2023-06-17T05:18:06ZengElsevierResults in Physics2211-37972023-07-0150106532Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical networkJoel Bruno Gonpe Tafo0Fabien Kenmogne1Alexandre Mando Kongne2Roger Eno3David Yemélé4Department of Base Scientists Education, Advanced Teacher Training College of the Technical Education, University of Douala, CameroonDepartment of Civil Engineering, Advanced Teacher Training College of the Technical Education, University of Douala, Cameroon; Corresponding author.Faculty of Science, University of Bamenda, Po Box 39 Bambili, Cameroon; Laboratory of Mechanics and modeling of Physical systems (L2MSP), Faculty of Sciences, University of Dschang, Box. 067, Dschang, CameroonDepartment of Civil Engineering, Advanced Teacher Training College of the Technical Education, University of Douala, CameroonLaboratory of Mechanics and modeling of Physical systems (L2MSP), Faculty of Sciences, University of Dschang, Box. 067, Dschang, CameroonWe investigate the propagation of modulated solitons in a two-dimensional (2D) nonlinear reaction diffusion electrical network with the intersite circuit elements (both in the propagation and transverse directions) acting as nonlinear resistances. Model equations for the circuit are derived and they reduce from the reductive perturbation technique to the 2D nonlinear dissipative Schrödinger equation governing the propagation of the small dissipative amplitude signals in the network. This equation does’nt have conserved quantities and it admits as solutions the 2D dissipative pulse and dark solitons, according to the sign of the product of dispersive and nonlinearity coefficients, with amplitude which narrows as the time increases. The exactness of the analytical analysis is confirmed by numerical simulations. Then by using the method of constants variation, the train of periodic pulse and dark solitons are also found, with their existence constraints also connected to the sign of the product of dispersive and nonlinearity coefficients, as found for standard pulse and dark solitons. Then the modulational instability (MI) criterion in system is found and is connected to the existence of modulated solitons.http://www.sciencedirect.com/science/article/pii/S221137972300325X2D dissipative NLS equationReaction diffusion NLTL2D transverse pulse soliton2D dark soliton |
| spellingShingle | Joel Bruno Gonpe Tafo Fabien Kenmogne Alexandre Mando Kongne Roger Eno David Yemélé Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network Results in Physics 2D dissipative NLS equation Reaction diffusion NLTL 2D transverse pulse soliton 2D dark soliton |
| title | Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network |
| title_full | Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network |
| title_fullStr | Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network |
| title_full_unstemmed | Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network |
| title_short | Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network |
| title_sort | modulated solitons and transverse stability in a two dimensional nonlinear reaction diffusion electrical network |
| topic | 2D dissipative NLS equation Reaction diffusion NLTL 2D transverse pulse soliton 2D dark soliton |
| url | http://www.sciencedirect.com/science/article/pii/S221137972300325X |
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