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F. Güngör

Publications and source records attributed to F. Güngör.

16 recordsLinked to original sources
arXiv2026

Noether symmetries and conservation laws of a class of time-dependent multidimensional nonlinear wave equations

Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational symmetries span a Euclidean algebra $\euclid(n)$ of space translations and rotations. They produce conservation of linear and angular momentums. For some specific forms of these two terms symmetry algebra is enlarged to a subalgebra of the conformal algebra $\conf(1,n)$ and in this case more interesting conservation laws are found.

math-ph↗
arXiv2024

A general class of invariant diffusion processes in one dimension

This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence of these symmetries are ensured, the transformation to canonical forms admitting either four- or six-dimensional symmetry groups and the full list of their infinitesimal generators are then immediately at our disposal without any cumbersome calculations that happen when at least one of the coefficients is arbitrarily chosen. We study in depth symmetry and reducibility properties and physically important solutions of six models arising in applications.

math-ph↗
arXiv2019

Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system

In this article, we construct novel explicit solutions for nonlinear Schrödinger systems with spatially inhomogeneous nonlinearity by means of the Lie symmetry method. We focus the attention to solutions with non-trivial phase, which have been scarcely considered in the related literature. To get started, the theoretical method based on Lie symmetries is exposed, thus reducing the problem to the integrability of an ODE. The non-trivial phase introduces a singular term into the ODE. Then, the method is used to construct new families of analytical solutions. Some illustrative examples are provided.

math-ph↗
arXiv2018

Analysis of the symmetry group and exact solutions of the dispersionless KP equation in $n+1$ dimensions

The Lie algebra of the symmetry group of the $(n+1)$-dimensional ge\-ne\-ra\-li\-zation of the dispersionless Kadomtsev--Petviashvili (dKP) equation is obtained and identified as a semi-direct sum of a finite dimensional simple Lie algebra and an infinite dimensional nilpotent subalgebra. Group transformation properties of solutions under the subalgebra $\Sl(2,\mathbb{R})$ are presented. Known explicit analytic solutions in the literature are shown to be actually group-invariant solutions corresponding to certain specific infinitesimal generators of the symmetry group.

nlin.SI↗
arXiv2018

Calculation of the propagator of Schrödinger's equation on $(0,\infty)$ with the potential $kx^{-2} + ω^2x^2$ by Lie symmetry group method

The propagators (fundamental solutions) of the heat and Schrödinger's equations on the half-line with a combined harmonic oscillator and inverse-square potential calculated in the recent paper [{\em J. Math. Phys.} {\bf 59}, 051507 (2018)] using Laplace's method are demonstrated to be obtainable alternatively within the framework of symmetry group methods discussed in a series of two papers in the same journal.

math-ph↗
arXiv2017

Linearizability for third order evolution equations

The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence of an infinite-dimensional symmetry group. Linearizing transformations for this class are found using symmetry structure and local conservation laws. A number of special cases as examples are discussed. Their transformation to equations within the same class by differential substitutions and connection with KdV and mKdV equations are also reviewed in this framework.

nlin.SI↗
arXiv2017

Lie point symmetry analysis of a second order differential equation with singularity

By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov-Pinney equation. In this context, nonlinear superposition rule for second order Kummer-Schwarz equation is rediscovered. Invariance under one-dimensional symmetry group is also used to obtain first integrals (Ermakov-Lewis invariants). Our motivation is a type of equations with singular term that arises in many applications, in particular in the study of general NLS (nonlinear Schrödinger) equations.

nlin.SI↗
arXiv2016

Variable coefficient Davey-Stewartson system with a Kac-Moody-Virasoro symmetry algebra

We study the symmetry group properties of the variable coefficient Davey-Stewartson (vcDS) system. The Lie point symmetry algebra with a Kac-Moody-Virasoro (KMV) structure is shown to be isomorphic to that of the usual (constant coefficient) DS system if and only if the coefficients satisfy some conditions. These conditions turn out to coincide with those for the vcDS system to be transformable to the DS system by a point transformation. The equivalence group of the vcDS system is applied to pick out the integrable subsystems from a class of non-integrable ones. Additionally, the full symmetry group of the DS system is derived explicitly without exponentiating its symmetry algebra. Lump solutions (rationally localized in all directions in $\mathbb{R}^2$) introduced by Ozawa for the DS system is shown to hold even for the vcDS system precisely when the system belongs to the integrable class, i.e. equivalent to the DS system. These solutions can be used for establishing exact blow-up solutions in finite time in the space $L^2(\mathbb{R}^2)$ in the focusing case.

nlin.SI↗
arXiv2014

Symmetries of 2+1-dimensional variable coefficient Burgers equations

We consider a class of variable coefficient Burgers equations in 2+1 dimensions and make use of their equivalence group to give a complete symmetry classification up to equivalence. Equivalence group is also applied to pick out the most general equation transformable to its constant coefficient form. The infinite-dimensional symmetry is used to transform the equation to a one-dimensional one.

nlin.SI↗
arXiv2012

Symmetry classification of variable coefficient cubic-quintic nonlinear Schrödinger equations

A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrödinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that their symmetry group can be at most four-dimensional in the genuine cubic-quintic nonlinearity. It is only five-dimensional (isomorphic to the Galilei similitude algebra gs(1)) when the equations are of cubic type, and six-dimensional (isomorphic to the Schrödinger algebra sch(1)) when they are of quintic type.

nlin.SI↗
arXiv2011

A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up of its solutions

A canonical variable coefficient nonlinear Schrödinger equation with a four dimensional symmetry group containing $\SL(2,\mathbb{R})$ group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the $L_p$-norm for $p>2$, $L_\infty$-norm and in the sense of distributions.

math.AP↗
arXiv2011

Variable coefficient nonlinear Schrödinger equations with four-dimensional symmetry groups and analysis of their solutions

Analytical solutions of variable coefficient nonlinear Schrödinger equations having four-dimensional symmetry groups which are in fact the next closest to the integrable ones occurring only when the Lie symmetry group is five-dimensional are obtained using two different tools. The first tool is to use one dimensional subgroups of the full symmetry group to generate solutions from those of the reduced ODEs (Ordinary Differential Equations), namely group invariant solutions. The other is by truncation in their Painlevé expansions.

nlin.SI↗
arXiv2010

Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras

We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.

nlin.SI↗