Soliton-like excitations in the one-dimensional electrical transmission line

S. E. Trullinger, V. E. Zakharov, and V. L. Pokrovsky, Solitons, North-Holland, Amsterdam (1986).

W. Eckhaus, Studies in the Nonlinear Stability Theory, Springer, Berlin (1965).

Y. S. Kivshar and M. Salerno, “Modulational instability in the discrete deformable nonlinear Schrödinger equation,” Phys. Rev. E, 49, 3543–3546 (1994).

M. Toda, “Theory of nonlinear lattice,” J. Phys. Soc. Jpn., 22, 413 (1967).

J. Parkes, “The modulation of weakly nonlinear dispersive waves near the marginal state of instability,” J. Phys. A: Math. Gen., 20, 2025–2036 (1987).

F. B. Pelap, T. C. Kofané, N. Flytzanis, and M. Remoissenet, “Waves modulations in the biinductance transmission line,” J. Phys. Soc. Jpn., 70, 2568–2577 (2001).

T. C. Kofané, B. Michaux, and M. Remoissenet, “Theoretical and experimental studies of diatomic lattice solitons using an electrical transmission line,” J. Phys. C, 21, 1395–1412 (1988).

M. Remoissenet, Waves Called Solitons, Springer, Berlin (1999).

P. Marquie, J. M. Bilbault, and M. Remoissenet, “Generation of envelope and hole solitons in an experimental transmission line,” Phys. Rev. E, 46, 828–835 (1994).

T. Taniuti and N. Yajima, “Perturbation method for nonlinear equations,” J. Math. Phys., 10, 1369–1372 (1969).

J. Ketchakeu, T. C. Kofané, and A. Zibi, “Modulational instability in an extended Φ 4 model near the marginal state,” Phys. Scr., 44, 505–510 (1991).

F. B. Pelap and T. C. Kofané, “The revised modulational instability criterion: I. The monoinductance transmission line,” Phys. Scr., 57, 410–415 (1998).

T. Kakutani and K. Michihiro, “Marginal state of modulational instability—note of the Benjamin-Feir instability,” J. Phys. Soc. Jpn., 52, 4129–4137 (1983).

T. Kawahara, J. Sakai, and T. Kakutani, “Nonlinear wave modulation in dispersive media,” J. Phys. Soc. Jpn., 29, 1068–1073 (1970).

R. Ndohi and T. C. Kofané, “Solitary waves in ferromagnetic chains near marginal state of instability,” Phys. Lett. A, 154, 377–379 (1991).

R. S. Johnson, Proc. Roy. Soc. A, 357, 131 (1977).

R. J. Deissler, J. Stat. Phys., 54, 1459 (1989).

Y. Pomeau, “Front motion, metastability and structural bifurcations in hydrodynamics,” Physica D, 23, 3–11 (1986).

T. B. Benjamin and J. F. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech., 27, 417–430 (1967).

J. T. Stuart and R. C. Di Prima, “The Eckhauss and Benjamin-Feir resonance mechanisms,” Phys. Roy. Soc. London. Ser. A, 362, 27–41 (1978).

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, London (1987).

F. B. Pelap and T. C. Kofané, “Modulational instability in some physical systems,” Phys. Scr., 64, 410–412 (2001).

E. Kengne, “Modified Ginzburg-Landau equation and Benjamin-Feir instability,” Nonlin. Oscillations, 6, No. 3, 346–356 (2003).

D. Pathria and J. L. Morris, “Exact solutions for a generalized nonlinear Schrödinger equation,” Phys. Scr., 39, 673–679 (1989).