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Cihangir Özemir

Publications and source records attributed to Cihangir Özemir.

6 recordsLinked to original sources
arXiv2026

Analysis of Lie symmetries and traveling wave solutions for the (2+1)-dimensional Boussinesq equation with general nonlinearity

In this study, we investigate Lie symmetries of the (2+1)-dimensional Boussinesq equation, which has been proposed to model the propagation of gravity waves on the water surface, with particular emphasis on the head-on collision of oblique waves. We consider this equation in a more general form involving an arbitrary function f(u) and establish a complete Lie symmetry classification with respect to the admissible forms of the nonlinearity. For the canonical equations arising from the classification, we construct reductions to ordinary differential equations by using an optimal system of two-dimensional subalgebras. Furthermore, we examine the exact solutions of the equation and analyze the stability of the traveling wave solutions.

nlin.SI↗
arXiv2021

Dispersionless Davey-Stewartson system: Lie symmetry algebra, symmetry group and exact solutions

Lie symmetry algebra of the dispersionless Davey-Stewartson (dDS) system is shown to be infinite-dimensional. The structure of the algebra turns out to be Kac-Moody-Virasoro one, which is typical for integrable evolution equations in $2+1$-dimensions. Symmetry group transformations are constructed using a direct (global) approach. They are split into both connected and discrete ones. Several exact solutions are obtained as an application of the symmetry properties.

nlin.SI↗
arXiv2020

Group Classification of a Higher-Order Boussinesq Equation

We consider a family of higher-order Boussinesq equations with an arbitrary nonlinearity. We determine the classes of equations so that a certain type of Lie symmetry algebra is admitted in this family. In case of a quadratic nonlinearity we provide several exact solutions, some of which are in terms of elliptic functions.

nlin.SI↗
arXiv2015

On Some Canonical Classes of Cubic-Quintic Nonlinear Schrödinger Equations

In this paper we bring into attention variable coefficient cubic-quintic nonlinear Schrödinger equations which admit Lie symmetry algebras of dimension four. Within this family, we obtain the reductions of canonical equations of nonequivalent classes to ordinary differential equations using tools of Lie theory. Painlevé integrability of these reduced equations is investigated. Exact solutions through truncated Painlevé expansions are achieved in some cases. One of these solutions, a conformal-group invariant one, exhibits blow-up behaviour in finite time in $L_p$, $L_\infty$ norm and in distributional sense.

nlin.SI↗