Stability of Negative Solitary Waves for a Generalized Camassa-Holm Equation with Quartic Nonlinearity

We consider the stability of negative solitary waves to a generalized Camassa-Holm equation with quartic nonlinearity. We obtain the existence of negative solitary waves for any wave speed > 0 and some of their qualitative properties and then prove that they are orbitally stable by using a method proposed by Grillakis et al

Soliton and periodic wave solutions to the osmosis K(2, 2) equation

In this paper, two types of traveling wave solutions to the osmosis K(2, 2) equation are investigated. They are characterized by two parameters. The expresssions for the soliton and periodic wave solutions are obtained.Comment: 14 pages, 16 figure

Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups

We formulate Euler-Poincar\'e equations on the Lie group Aut(P) of automorphisms of a principal bundle P. The corresponding flows are referred to as EPAut flows. We mainly focus on geodesic flows associated to Lagrangians of Kaluza-Klein type. In the special case of a trivial bundle P, we identify geodesics on certain infinite-dimensional semidirect-product Lie groups that emerge naturally from the construction. This approach leads naturally to a dual pair structure containing \delta-like momentum map solutions that extend previous results on geodesic flows on the diffeomorphism group (EPDiff). In the second part, we consider incompressible flows on the Lie group of volume-preserving automorphisms of a principal bundle. In this context, the dual pair construction requires the definition of chromomorphism groups, i.e. suitable Lie group extensions generalizing the quantomorphism group.Comment: 52 pages; revised versio

On Compact and Noncompact Structures for the Improved Boussinesq Water Equations

The nonlinear variants of the generalized Boussinesq water equations with positive and negative exponents are studied in this paper. The analytic expressions of the compactons, solitons, solitary patterns, and periodic solutions for the equations are obtained by using a technique based on the reduction of order of differential equations. It is shown that the nonlinear variants, or nonlinear variants together with the wave numbers, directly lead to the qualitative change in the physical structures of the solutions

Lineer olmayan sobolev türü kısmi türevli diferansiyel denklemlerin tanh-coth yöntemi ile çözümü

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Birçok fiziksel olguyu açıklayan Sobolev türü denklemler, boyuta ve zamana bağlı türevleri, en yüksek mertebeden türevli terimlerinde bulundurmaları ile karakterize edilmektedir. En yüksek mertebeli türevlerinde sadece bir tane zamana bağlı türev bulunduran denklemler ise pseudoparabolik denklem olarak adlandırılır ve bu denklemler Sobolev türü denklemlerin özel bir durumudur. Bu çalıĢmada iyi bilinen Sobolev ve pseudoparabolik denklem türleri ele alınmıĢ ve bu denklemlerin genel özellikleri verilmiĢtir. Tanh-coth yöntemi lineer olmayan kısmi türevli diferansiyel denklemlerin hareketli dalga çözümlerini bulmada etkili ve güvenilir bir yöntemdir. Bugüne kadar bu yöntem yoğun olarak kullanılmıĢ ve yöntemin Riccati denklemi kullanılarak elde edilen modifikasyonları literatürde tartıĢılmıĢtır. Bu tezde, tanh-coth yönteminin temel özellikleri ve bu yöntemin diğer uzantıları ele alınmıĢtır. Buna ek olarak tanhcoth yöntemi, sembolik hesaplama sistemleri yardımıyla Sobolev türü denklemlerin tam çözümlerini araĢtırmada kullanılmıĢ ve bu denklemlerin birçok hareketli dalga çözümü elde edilmiĢtir. Elde edilen bu sonuçlar daha önce elde edilen bilgilerin bir doğrulaması ve geliĢtirilmesi olarak görülebilir. ÇalıĢma boyunca, cebirsel iĢlemler için Maple ve Scientific Work Place programları kullanılmıĢtır.Sobolev type equations have been used to describe many physical phenomena and they are characterized by having mixed time and space derivatives appearing in the highest-order terms of an partial differential equation. Equations with a one time derivative appearing in the highest order term are called pseudoparabolic and they are special case of Sobolev equations. In this work, well-known Sobolev and pseudoparabolic type equations have been considered and general properties of these equations have been given. The tanh-coth is a powerful and reliable technique for finding travelling wave solutions for nonlinear partial differential equations. This method has been used extensively and it was subjected by some modifications using the Riccati equation. The main features of the tanh-coth method and various extension forms of this method have been discussed in this thesis. Furthermore, the tanh-coth method with the aid of symbolic computational systems has been employed to investigate exact solutions of Sobolev type equations and abundant travelling wave solutions have been found. The results obtained can be viewed as a verification and improvement of the previously known data. Throughout the study, Maple and Scientific Work Place was used to deal with the tedious algebraic operations

Nonlinear Waves and Dispersive Equations

The aim of the workshop was to discuss current developments in nonlinear waves and dispersive equations from a PDE based view. The talks centered around rough initial data, long time and global existence, perturbations of special solutions, and applications

Laboratory-directed research and development: FY 1996 progress report

This report summarizes the FY 1996 goals and accomplishments of Laboratory-Directed Research and Development (LDRD) projects. It gives an overview of the LDRD program, summarizes work done on individual research projects, and provides an index to the projects` principal investigators. Projects are grouped by their LDRD component: Individual Projects, Competency Development, and Program Development. Within each component, they are further divided into nine technical disciplines: (1) materials science, (2) engineering and base technologies, (3) plasmas, fluids, and particle beams, (4) chemistry, (5) mathematics and computational sciences, (6) atomic and molecular physics, (7) geoscience, space science, and astrophysics, (8) nuclear and particle physics, and (9) biosciences