Animation of a
wave-packet solution of the Eckhaus equation. The blue line is the
real part of the solution, the red line is the
imaginary part and the black line is the
wave envelope (
absolute value). Note the
asymmetry in the envelope for the Eckhaus equation, while the envelope – of the corresponding solution to the linear Schrödinger equation – is symmetric (in ). The short waves in the packet propagate faster than the long waves.Animation of the
wave-packet solution of the
linear Schrödinger equation – corresponding with the above animation for the Eckhaus equation. The blue line is the
real part of the solution, the red line is the
imaginary part, the black line is the
wave envelope (
absolute value) and the green line is the
centroid of the wave packet envelope.
Eckhaus, W. (1985), The long-time behaviour for perturbed wave-equations and related problems, Department of Mathematics, University of Utrecht, Preprint no. 404. Published in part in: Eckhaus, W. (1986), "The long-time behaviour for perturbed wave-equations and related problems", in Kröner, E.; Kirchgässner, K. (eds.), Trends in applications of pure mathematics to mechanics, Lecture Notes in Physics, vol. 249, Berlin: Springer, pp. 168–194,
doi:
10.1007/BFb0016391,
ISBN978-3-540-16467-8
Kundu, A. (1984), "Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations", Journal of Mathematical Physics, 25 (12): 3433–3438,
Bibcode:
1984JMP....25.3433K,
doi:
10.1063/1.526113
Taghizadeh, N.; Mirzazadeh, M.; Tascan, F. (2012), "The first-integral method applied to the Eckhaus equation", Applied Mathematics Letters, 25 (5): 798–802,
doi:10.1016/j.aml.2011.10.021
Zwillinger, D. (1998), Handbook of differential equations (3rd ed.), Academic Press,
ISBN978-0-12-784396-4
Animation of a
wave-packet solution of the Eckhaus equation. The blue line is the
real part of the solution, the red line is the
imaginary part and the black line is the
wave envelope (
absolute value). Note the
asymmetry in the envelope for the Eckhaus equation, while the envelope – of the corresponding solution to the linear Schrödinger equation – is symmetric (in ). The short waves in the packet propagate faster than the long waves.Animation of the
wave-packet solution of the
linear Schrödinger equation – corresponding with the above animation for the Eckhaus equation. The blue line is the
real part of the solution, the red line is the
imaginary part, the black line is the
wave envelope (
absolute value) and the green line is the
centroid of the wave packet envelope.
Eckhaus, W. (1985), The long-time behaviour for perturbed wave-equations and related problems, Department of Mathematics, University of Utrecht, Preprint no. 404. Published in part in: Eckhaus, W. (1986), "The long-time behaviour for perturbed wave-equations and related problems", in Kröner, E.; Kirchgässner, K. (eds.), Trends in applications of pure mathematics to mechanics, Lecture Notes in Physics, vol. 249, Berlin: Springer, pp. 168–194,
doi:
10.1007/BFb0016391,
ISBN978-3-540-16467-8
Kundu, A. (1984), "Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations", Journal of Mathematical Physics, 25 (12): 3433–3438,
Bibcode:
1984JMP....25.3433K,
doi:
10.1063/1.526113
Taghizadeh, N.; Mirzazadeh, M.; Tascan, F. (2012), "The first-integral method applied to the Eckhaus equation", Applied Mathematics Letters, 25 (5): 798–802,
doi:10.1016/j.aml.2011.10.021
Zwillinger, D. (1998), Handbook of differential equations (3rd ed.), Academic Press,
ISBN978-0-12-784396-4