Modulated solitons and transverse stability in a two-dimensional nonlinear reaction diffusion electrical network

• Published in: Results in physics 2023-07, Vol.50, p.106532, Article 106532
• Main Authors: Tafo, Joel Bruno Gonpe, Kenmogne, Fabien, Kongne, Alexandre Mando, Eno, Roger, Yemélé, David
• Format: Article
• Language: English
• Subjects: 2D dark soliton; 2D dissipative NLS equation; 2D transverse pulse soliton; Reaction diffusion NLTL
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2023.106532

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. •The dynamics of modulated waves in the 2D reaction diffusion NLTL is investigated.•The 2D NLTL has intersite circuit elements acting as nonlinear resistances•The 2D dissipative NLS equation is derived,it doesn't admit conserved quantities•The 2D dissipative pulse and dark solitons as solutions and the MI are found•The periodic solitons are found using the methods of constants variations