Existence of Homoclinic Travelling Waves in Infinite Lattices
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4
By using critical point theory, we investigate the existence of homoclinic travelling waves in an one-dimensional infinite lattice with nearest-neighbor interactions and a on-site potential (density) $f$. The system is described by the infinite system of second-order differential equations:
where $f,V\in C^{1}(\mathbb{R},\mathbb{R})$. We establish three new criteria ensuring the existence of non-trivial homoclinic travelling wave solutions, for any given speed $c$ bigger (or smaller) than some constant depending on $f$ and $V$. Relevant results in the literatures are extended.
| $\ddot{q}_{j}+f'(q_{j}(t))=V'(q_{j+1}(t)-q_{j}(t))-V'(q_{j}(t)-q_{j-1}(t)), \quad t\in\mathbb{R}, \ j\in\mathbb{Z},$ |
Classification :
37K60, 34C25, 34C37
@article{BMMS_2013_36_4_a10,
author = {Zhisu Liu and Shangjiang Guo and Ziheng Zhang},
title = {Existence of {Homoclinic} {Travelling} {Waves} in {Infinite} {Lattices}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2013},
volume = {36},
number = {4},
url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_4_a10/}
}
Zhisu Liu; Shangjiang Guo; Ziheng Zhang. Existence of Homoclinic Travelling Waves in Infinite Lattices. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2013_36_4_a10/