Abstract
We use path-following methods and spectral collocation methods to study families of solitary wave solutions of lattice equations. These techniques are applied to a number of 1-D and 2-D lattices, including an electrical lattice introduced by Remoissenet and co-workers, and a 2-D lattice suggested by Zakharov, which in a particular continuum limit reduces to the Kadomtsev-Petviashvili equation.
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References
M Toda. Theory of Nonlinear Lattices. Springer, Berlin, 1981.
M J Ablowitz and J F Ladik. A nonlinear difference scheme and inverse scattering. Stud. Appl. Math., 55:213–229, 1976.
J C Eilbeck and R Flesch. Calculation of families of solitary waves on discrete lattices. Phys. Lett. A, 149:200–202, 1990.
C Canuto, M Y Hussaini, A Quarteroni, and T A Zang. Spectral Methods in Fluid Mechanics. Springer-Verlag, Berlin, 1988.
R Seydel. From Equilibrium to Chaos — Practical Bifurcation and Stability Analysis. Elsevier, London, 1988.
D Hochstrasser, F G Mertens, and H Büttner. An iterative method for the calculation of narrow solitary excitations on atomic chains. Physica, D35:259–266, 1989.
D B Duncan, C H Walshaw, and J A D Wattis. A symplectic solver for lattice equations. (these proceedings), 1991.
M Remoissenet and B Michaux. Electrical transmission lines and soliton propagation in physical systems. In G. Maugin, editor, Continuum Models and Discrete Systems, Proceedings of the CMDS6 Conference, Dijon 1989, London, 1990. Longman.
P L Christiansen and A C Scott. Davydov's Soliton Revisited. Plenum, New York, 1990.
J C Eilbeck, P S Lomdahl, and A C Scott. The discrete self-trapping equation. Physica D: Nonlinear Phenomena, 16:318–338, 1985.
H Feddersen. Solitary wave solutions to the discrete nonlinear Schrödinger equation. (these proceedings), 1991.
O A Druzhinin and L A Ostrovskii. Solitons in discrete lattices. Preprint, to be published in Phys. Lett. A, 1991.
D B Duncan, J C Eilbeck, C H Walshaw, and V E Zakharov. Solitary waves on a strongly anisotropic KP lattice. Submitted to Phys. Lett. A., 1991.
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© 1991 Springer-Verlag
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Eilbeck, J.C. (1991). Numerical studies of solitons on lattices. In: Remoissenet, M., Peyrand, M. (eds) Nonlinear Coherent Structures in Physics and Biology. Lecture Notes in Physics, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54890-4_165
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DOI: https://doi.org/10.1007/3-540-54890-4_165
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