TY - JOUR

T1 - Improved models of dense anharmonic lattices

AU - Rosenau, P.

AU - Zilburg, A.

N1 - Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/1/15

Y1 - 2017/1/15

N2 - We present two improved quasi-continuous models of dense, strictly anharmonic chains. The direct expansion which includes the leading effect due to lattice dispersion, results in a Boussinesq-type PDE with a compacton as its basic solitary mode. Without increasing its complexity we improve the model by including additional terms in the expanded interparticle potential with the resulting compacton having a milder singularity at its edges. A particular care is applied to the Hertz potential due to its non-analyticity. Since, however, the PDEs of both the basic and the improved model are ill posed, they are unsuitable for a study of chains dynamics. Using the bond length as a state variable we manipulate its dispersion and derive a well posed fourth order PDE.

AB - We present two improved quasi-continuous models of dense, strictly anharmonic chains. The direct expansion which includes the leading effect due to lattice dispersion, results in a Boussinesq-type PDE with a compacton as its basic solitary mode. Without increasing its complexity we improve the model by including additional terms in the expanded interparticle potential with the resulting compacton having a milder singularity at its edges. A particular care is applied to the Hertz potential due to its non-analyticity. Since, however, the PDEs of both the basic and the improved model are ill posed, they are unsuitable for a study of chains dynamics. Using the bond length as a state variable we manipulate its dispersion and derive a well posed fourth order PDE.

KW - Anharmonic lattices

KW - Compactons

KW - Improved PDE description

KW - Quartic and Hertz potentials

UR - http://www.scopus.com/inward/record.url?scp=84995642124&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2016.10.051

DO - 10.1016/j.physleta.2016.10.051

M3 - מאמר

AN - SCOPUS:84995642124

VL - 381

SP - 87

EP - 93

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2

ER -