Group classification and exact solutions of a higher-order Boussinesq equation

Yasin Hasanoğlu, Cihangir Özemir*

*Bu çalışma için yazışmadan sorumlu yazar

Araştırma sonucu: ???type-name???Makalebilirkişi

4 Atıf (Scopus)

Özet

We consider a family of sixth-order Boussinesq equations in one space dimension with an arbitrary nonlinearity. The equation was originally derived for a one-dimensional lattice model considering higher order effects, and later it was re-derived in the context of nonlinear nonlocal elasticity. In the sense of one-dimensional wave propagation in solids, the nonlinearity function of the equation is connected with the stress-strain relation of the physical model. Considering a general nonlinearity, we determine the classes of equations so that a certain type of Lie symmetry algebra is admitted in this family. We find that the maximal dimension of the symmetry algebra is four, which is realized when the nonlinearity assumes some special canonical form. After that we perform reductions to ordinary differential equations. In case of a quadratic nonlinearity, we provide several exact solutions, some of which are in terms of elliptic functions.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)2599-2611
Sayfa sayısı13
DergiNonlinear Dynamics
Hacim104
Basın numarası3
DOI'lar
Yayın durumuYayınlandı - May 2021

Bibliyografik not

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

Parmak izi

Group classification and exact solutions of a higher-order Boussinesq equation' araştırma başlıklarına git. Birlikte benzersiz bir parmak izi oluştururlar.

Alıntı Yap