Solitons in a nonlinear elastic medium

Journal Article · Fri Feb 01 04:00:00 EST 1991 · Physical Review, B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.43.3493· OSTI ID:5863636

Kivshar, Y S ^[1]

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1. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (US)

The influence of nonlinearity on shear horizontal elastic (bulk and surface) waves in crystals is considered on the basis of a nonlinear equation derived from a microscopic scalar model. The continuum limit is compared with the equation obtained in the framework of nonlinear elasticity theory. Using the equation, it is demonstrated that nonlinear surface waves of the shear horizontal polarization are modulationally unstable, and, therefore, they have to produce surface solitary waves. The solitons are studied in the case of a nonlinear elastic plate when the effective asymptotic technique may be elaborated. In the main approximation of the asymptotic approach, the effective nonlinear Schroedinger equation is derived. We predict that in the nonlinear elastic plate it is possible to observe bright or dark envelope solitons that propagate without distortion. The properties of the solitons depend on the carrier wave number and the thickness of the plate. We demonstrate also that there is a discrete set of the solitons produced by linear modes of the elastic plate.

• OSTI ID: 5863636
• Journal Information: Physical Review, B: Condensed Matter; (USA), Journal Name: Physical Review, B: Condensed Matter; (USA) Vol. 43:4; ISSN 0163-1829; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTALS
DIFFERENTIAL EQUATIONS
EQUATIONS
NONLINEAR PROBLEMS
OPTICAL PROPERTIES
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PLATES
QUANTUM ELECTRONICS
QUASI PARTICLES
SCHROEDINGER EQUATION
SOLITONS
WAVE EQUATIONS