1,721,013 research outputs found
On KKLT/CFT and LVS/CFT dualities
Full text linkWe present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifi- cations. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both cases we identify the large ‘central charge’, find a separation of scales between the radius of AdS and the size of the extra dimensions and show that the dual CFT has only a limited number of operators with small conformal dimension. Differences between the two sets of duals are identified. Besides a different amount of supersymmetry (N = 1 for KKLT and N = 0 for LVS) we find that the LVS CFT dual has only one scalar operator with O(1) conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of h1,1 K ̈ahler moduli have this property. Also, the maximal number of degrees of freedom is estimated to be larger in LVS than in KKLT duals. In both cases we explic- itly compute the coefficient of the logarithmic contribution to the one-loop vacuum energy which should be invariant under duality and therefore provides a non-trivial prediction for the dual CFT. This coefficient takes a particularly simple form in the KKLT case
Classical Method for Some Nonlinear Systems
No full textThe objective of this thesis entitled, “Classical method for some nonlinear systems ”, is to obtain the Lie symmetries and the exact solutions of nonlinear partial differential equations (PDEs) or their systems, which represent some of the important physical phenomenon
Exact Travelling Wave Solution of Some Nonlinear Partial Differential Equations
No full textM.Sc. (Mathematics and Computing)Exact solutions to nonlinear partial differential equations play an important role for
understanding of qualitative as well as quantitative features of many phenomena and
processes. Exact solutions visually demonstrate and make it possible to understand the
mechanism of complex nonlinear effects.
The thesis entitled “Exact Travelling Wave Solutions of Some Nonlinear Partial
Differential Equations” is an attempt to obtain the exact solutions of some nonlinear
partial differential equations. The thesis has been divided into six chapters. The brief
outline of the research work presented chapter wise in the thesis is as follows:
First chapter is introductory in nature, in this chapter, definition of nonlinear
differential equations and basic concepts are discussed. A brief summary of literature
available on the subject and summary of the work presented in the thesis also appears in
this chapter. In the second chapter, methodology of ÷
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expansion method. We have successfully derived two type of travelling wave solution in
term of hyperbola and trigonometric functions for the generalized sinh-Gorden equation by
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The fourth chapter comprises Huber’s equation with solved by ÷
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method and in fifth chapter we have obtained exact travelling wave solution of ZK-BBM
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In the sixth chapter Boussinesq equation has been solved with the modified ÷
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expansion method. We have successfully derived travelling wave solution in term of
trigonometric functions for the generalized Boussinesq equation by using the modified
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It is worth to mention that all the solutions reported in this thesis are new and
authenticity of the solutions is checked by Maple software
Symmetry Reduction Method for Exact Solutions of Some Nonlinear Systems
No full textThe Thesis entitled “SYMMETRY REDUCTION METHOD FOR EXACT
SOLUTIONS OF SOME NONLINEAR SYSTEMS” is attempted to find some exact
solutions of nonlinear systems of partial differential equations (PDEs) governing some
important physical phenomenons by using Symmetry reduction method which is based
on Fréchet derivatives of the differential operators and we drive Lie algebra which then
helps us to obtain the optimal system of generators. Then, we find reduced ordinary
differential equations (ODEs) from given nonlinear PDEs equations and some exact
solutions of them.SMC
Symmetries and Exact Solutions of Some Systems of Nonlinear Partial Differential Equations by Lie Classical Method
No full textMS, SMCAThe objective of this thesis entitled, “ Symmetries and Exact Solutions of Some Systems of Nonlinear Partial Differential Equations by Lie Classical Methods”, is to obtain the Lie symmetries
and the exact solutions of nonlinear partial differential equations or their systems, which represent
some of the important physical phenomenon. The nonlinear phenomena are encountered in a variety
of situations in physics as well as in other natural applied sciences. Most of these phenomena are governed by nonlinear partial differential equations
Exact Solutions and Painleve Analysis of some Nonlinear Partial Differential Equations
No full textDoctor of Philosophy- MathematicsThe integrability of nonlinear partial differential equations has been addressed in
this thesis. The various approaches for complete integrability have been comprehensively exploited for important equations in mathematical physics. Along with usual the Lie symmetry analysis, a detailed discussion on various group classification techniques has been given. More general symmetries for variable coefficient coupled KdV equations have been reported. Based on Lie algebra isomorphism, an obscured technique for Lie algebra classification has been re-introduced to improve existing Lie algebra classifications. Motivated by the powerful Hirota's bilinear method, a new test function has been proposed which generalizes the existing test functions for finding exact solutions of PDEs. The Hirota's bilinear method has also been used to find Backlund transformations, Lax system, an infinite number of nontrivial conservation laws. Using direct method and new conservation theorem, nontrivial conservation laws have been constructed for some important PDEs of physical relevance
Symmetry Analysis and Conservation Laws for Some Systems of Nonlinear Partial Differential Equations
No full textThe work complied in this thesis includes the investigation of nonlinear partial differential equations (PDEs) of integer and fractional order representing some physical phenomena for exact solutions, symmetries, and conservation laws. Linear dispersion analysis of fractional order PDEs is carried out to identify the normal/anomalous dispersion of waves. The techniques to retrieve solutions have thoroughly described and successfully implemented. The thesis consists of five chapters compiled for the investigation of seven nonlinear PDEs which are (2+1)-dimensional new coupled Zakharov-Kuznetsov (ZK) system, generalised order Korteweg and de Vries (KdV) equation, new coupled ZK system as well as Wu-Zhang system in (2+1)-dimensions having time derivatives of fractional order, time fractional order equation from Burgers hierarchy, space-time fractional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation and space-time fractional Maccari model in (2+1)-dimensions. Thesis is organised into five chapters. The chapter 1 introduces some important nonlinear PDEs of integer and fractional orders. The physical phenomena inherited by different types of PDEs are tabulated. Brief literature reviews on Lie group of transformations, methods for finding exact solutions, and conservation laws are presented. Introduction of linear dispersion analysis is briefed out. The frame work of the thesis is also presented systematically in this chapter. The chapter 2 consists the preliminaries including some definitions, theorems related to Lie group theory, conservation laws, exact solutions, and dispersion analysis. Lie infinitesimal criterion to examine integer and time fractional PDEs is presented in an algorithmic way. The various methodologies used for finding solutions in terms of solitary waves, exact travelling waves, and doubly periodic waves have thoroughly described. Also, method known as improved F-expansion is proposed for examining the space-time fractional PDEs and subsequently, applied to space-time fractional potential YTSF equation in chapter 5. The methods to derive conservation laws for nonlinear PDEs have been discussed in details and algorithms are constructed for the same. For fractional PDEs, the linear dispersion analysis is also suggested. The chapter 3 is devoted to study the integer order nonlinear PDEs with variable coefficients such as (2+1)-dimensional new coupled ZK system and generalised order KdV equation. The infinitesimal symmetries, symmetry groups, optimal system, invariants and reductions are systematically determined for new coupled ZK system. The variety of solutions in terms of Jacobi, trigonometric and hyperbolic functions are obtained, and analysed graphically to discuss the effect of arbitrary function on the wave profile. The generalised order KdV equation is also examined for Lie symmetries. Vector fields of the optimal system give solutions in an explicit form appeared as power series and involved Jacobi elliptic functions. The conservation laws are constructed for these equations by applying direct method and new conservation theorem with nonlinear self-adjointness. The chapter 4 presents the comprehensive investigation of nonlinear PDEs having time derivatives of fractional order. It includes new coupled ZK system in (2+1)-dimensions, Wu-Zhang system in (2+1)-dimensions and order equation from Burgers hierarchy. The Lie classical technique is adopted to examine Lie symmetries with the use of Riemann-Liouville fractional (RLF) order derivative and corresponding invariants for these equations. The dimensions of fractional PDEs are reduced from (2+1) to (1+1) using invariants. The solutions show bright, dark and singular solitary wave like character for new coupled ZK system. The methodology of exponential rational function method has been utilized to seek solutions of Wu-Zhang system. Solutions in form of power series have obtained for order equation from Burgers hierarchy. The solutions of these equations are discussed graphically. The conservation laws for the equations are obtained by new conservation theorem. These equations are also studied for deriving dispersion relations, group and phase velocities. The chapter 5 deals with important nonlinear PDEs from mathematical physics having space-time variations of fractional form such as potential YTSF equation and (2+1)-dimensional Maccari system. The improved F-expansion method suggested in chapter 2 for space-time fractional PDEs is applied to potential YTSF equation in this chapter and exact travelling waves are obtained as solutions. The Maccari system in (2+1)-dimensions is investigated using an extended Jacobi elliptic function expansion (EJEFE) method for deriving solutions having doubly periodic waves. The solutions of these equations are discussed graphically to show the influence of fractional parameters onto wave profile. The dispersion relations for space-time fractional PDEs are systematically derived and the anomalous/normal dispersion of waves is shown graphically. At last, the summary of the thesis and some concluding remarks are given of the work conducted in different chapters
Group Theoretic Techniques for Solutions of Einstein Equations
No full textDoctor of Philosophy-ThesisGeneral relativity is a physical theory which plays a key role in astrophysics and is impor-
tant for a number of ambitious experiments and space missions. Einstein field equations
are basic equations of general relativity and are expressed in terms of coupled highly non-
linear partial differential equations describing the matter content of space-time. For this
reason it is clear that the theory of partial differential equations is of immense importance
in the study of Einstein field equations. The investigations carried out are confined to
the applications of the group-theoretic methods, symmetry reduction method, Painlev´e
analysis and Generalized G′
G - expansion method to the system of nonlinear partial differ-
ential equations arising in general relativity and other important physical phenomenon
from mathematical physics.
The thesis entitled GROUP THEORETIC TECHNIQUES FOR SOLUTIONS
OF EINSTEIN EQUATIONS comprises eight chapters. This thesis is a condensed re-
view of the exact solutions of Einstein field equations and ensuing phenomena.School of Mathematics and Computer Applications, Thapar University, Patial
Symmetry Reduction Method for Nonlinear Partial Differential Equations
No full textMaster of Science (Mathematics and Computing)This Thesis entitled “SYMMETRY REDUCTION METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS” is aimed to derive exact solutions of some nonlinear partial differential equations (PDEs) by the using Symmetry reduction methods. By using this method, symmetries are obtained which helps us to construct optimal system of generators. After that partial differential equations are reduced to ordinary differential equations (ODEs) and exact solutions corresponding to these ordinary differential equations are obtained.School of Mathematics and Computer Applications, Thapar University, Patial
Exact Solutions of Nonlinear Partial Differential Equations
No full textM.Sc. ( Mathematics and Computing)The thesis entitled “ EXACT SOLUTIONS OF NONLINEAR PARTIAL
DIFFRENTIAL EQUATIONS ” is an attempt to obtain the exact solutions of some
nonlinear partial differential equations.SMC
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