Geodesic
Existence of Homoclinic Travelling Waves in Infinite Lattices
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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:

$\ddot{q}_{j}+f'(q_{j}(t))=V'(q_{j+1}(t)-q_{j}(t))-V'(q_{j}(t)-q_{j-1}(t)), \quad t\in\mathbb{R}, \ j\in\mathbb{Z},$

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.
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/}
}
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AU  - Zhisu Liu
AU  - Shangjiang Guo
AU  - Ziheng Zhang
TI  - Existence of Homoclinic Travelling Waves in Infinite Lattices
JO  - Bulletin of the Malaysian Mathematical Society
PY  - 2013
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/BMMS_2013_36_4_a10/
ID  - BMMS_2013_36_4_a10
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%A Shangjiang Guo
%A Ziheng Zhang
%T Existence of Homoclinic Travelling Waves in Infinite Lattices
%J Bulletin of the Malaysian Mathematical Society
%D 2013
%V 36
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%F 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/