Search or add a thesis

Advanced Search (Beta)
Home > Darboux Transformation and Discrete Integrable Systems: Approach to Soliton Solutions

Darboux Transformation and Discrete Integrable Systems: Approach to Soliton Solutions

Thesis Info

Access Option

External Link

Author

Riaz, Hafiz Wajahat Ahmed

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Physics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11061/1/hafiz%20wajhat%20ahmad%20riaz_Physics_2019_UoP_Punjab_22.04.2019.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725811203

Similar


In this thesis, we study some discrete and semi-discrete integrable systems from a point of view of Lax pair representation and Darboux transformation. We shall investigate discretizationofprincipalchiralequations,generalizedHeisenbergmagnetmodel,generalized coupled dispersionless systems and short-pulse equations and give their Lax pair representations. Using a quasideterminant Darboux transformation matrix approach, we construct multisoliton solutions of the above mentioned systems. Darboux transformation is defined for the matrix solutions of the respective discrete equations in terms of matrix solutions to the Lax pair and are expressed in terms of quasideterminants. To get more insight, we shall discuss the comparison of discrete models with their respective continuous models. We show that discrete model can be reduced to continuous model, not only on the level of nonlinear evolution equation, but also on the level of solutions by applying the appropriate continuumlimit. Bystudyingvariousnewmodels,weshallcomputeexplicitexpressionsof multisoliton solutions including kink-soliton, dark-soliton, bright-soliton, loop-soliton and cuspon-soliton solutions.
Loading...

Similar Thesis

Showing 1 to 20 of 100 entries
TitleAuthorSupervisorDegreeInstitute
PhD
University of the Punjab, Lahore, Pakistan
Mphil
Government College University, Lahore, Pakistan
PhD
National College of Business Administration and Economics, Lahore, Pakistan
Mphil
Riphah International University, Faisalabad, Pakistan
PhD
HITEC University, Taxila, Pakistan
University of Utah, Salt Lake City, United States of America
PhD
University of the Punjab, Lahore, Pakistan
BSc
University of Management and Technology, Lahore, Pakistan
PhD
Capital University of Science & Technology, Islamabad, Pakistan
PhD
Government College University, Lahore, Pakistan
PhD
Government College University, Lahore, Pakistan
PhD
University of Engineering and Technology, Lahore, Pakistan
PMT
COMSATS University Islamabad, Islamabad, Pakistan
PhD
COMSATS University Islamabad, Islamabad, Pakistan
Mphil
Quaid-i-Azam University, Islamabad, Pakistan
PhD
COMSATS University Islamabad, Islamabad, Pakistan
MS
Capital University of Science & Technology, Islamabad, Pakistan
MS
International Islamic University, Islamabad, Pakistan
Mphil
Quaid-i-Azam University, Islamabad, Pakistan
PhD
University of Peshawar, Peshawar, Pakistan
TitleAuthorSupervisorDegreeInstitute
Showing 1 to 20 of 100 entries

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

نواب عالی مرحوم

نواب عالی مرحوم
صاحبزادہ مرزا حاجی ضمیر الدین صاحب عالی مرحوم نواب علاء الدین خاں صاحب علائی کے چوتھے اورسب سے چھوٹے لڑکے تھے۔مرحوم میں وہ تمام خوبیاں موجود تھیں جواگلے بزرگوں میں ہوتی تھیں۔ وہ خاندان کے ایک ایسے فرد تھے جن کی موت نے خاندان پریہ واضح کردیا کہ اب اس کمی کوپورا کرنا بالکل ناممکن ہے۔
میرے رشتے کے ماموں تھے لیکن ان کی بزرگانہ شفقت ایسی تھی کہ حقیقی ماموؤں سے بڑھ کر تھی۔عربی فارسی کے متبحر عالم تھے نہ صرف عالم تھے بلکہ عالم باعمل۔ ان کے دل میں خدا کی تمام مخلوق کے دکھ سکھ کاپورا پورا خیال تھا۔ان کی موت سے بہت سی لاوارث عورتیں شکستہ دل ہوئیں اور بیکس یتیم بے سہارا رہ گئے۔ مرحوم کے حالات ذیل ان کے بھتیجے صاحبزادہ شمس الدین احمدخاں صاحب دیوان ریاست لوہارونے لکھ کر بھیجے ہیں جس کے لیے میں موصوف کی شکرگزار ہوں۔
آپ ۱۶؍دسمبر ۱۸۶۷ء کودہلی میں پیدا ہوئے۔ فخرالدولہ نواب علاء الدین احمدخاں بہادر فرمانروائے لوہارو کے پانچویں فرزند اورسب سے چھوٹے بیٹے تھے۔ آپ کے باپ نے پیدائش کے وقت اپنی بیاض میں یہ درج فرمالیا تھا: ’’ تولدپسرِکامگار ہوشیار مرزا ضمیر الدین احمدخاں طال عمرہ درساعتِ سُنبلہ از بطنِ شمس النسا بیگم۔
مرزا غالب کے تعلقِ خاص کی تقریب سے نواب علاء الدین احمدخاں علائی کو دنیا جانتی ہے۔ شمس النساء بیگم دخترِ نواب جلال الدین خاں نبیرۂ امیرالامراء نواب نجیب الدولہ رئیس نجیب آباد ہیں۔ مرزا ضمیرالدین احمدخاں کی تعلیم وتربیت زیرِ نگرانی والد بزرگوار ہوئی۔بعض استاد ایرانی تھے۔ مثلاً مرزا ابو طالب شیرازی ابن سید ہاشم نجفی۔ نوعمری میں گھوڑے کی سواری کاشوق ہوا۔ لوہارومیں جرنیل صاحب کے لقب سے مشہور ہوئے۔ گھوڑوں کی شناخت میں کمال رکھتے تھے۔اسلحہ کی شناخت میں خاص مہارت تھی۔خود گولی، بارود اور بندوق کی ٹوپیاں بنالیتے تھے۔ ریاست...

Academic Research on Non- Muslim Religious Minorities Content analysis of the Research papers from a Pakistani Perspective

This study aims to examine research papers on religious minorities to determine their issues, rights, and privileges in Pakistan. In a civilized society, everyone has basic rights regardless of race, color, or religion. Everyone has cultural, political, religious, and constitutional freedom in a peaceful society. In general, it is perceived that, in Pakistan, followers of other religions than Islam are not given their essential rights, especially regarding their religious rights. To secure minority participation in decision-making, they may reserve seats in administration and parliament, organize national and local minority consultative organizations, and provide cultural or territorial autonomy. In the context of Pakistan, the school curriculum and state policies are viewed as the primary causes of prejudice against minorities. However, numerous other elements may contribute to the establishment of attitudes about them. Therefore, in order to reveal and appropriately address the issue, this study will use qualitative research methodology with an analytical research approach. Rights, issues, and problems of minorities have been a matter of concern to various scholars, states, and societies throughout history and in the contemporary era too. The study suggests that there should be made awareness at the grassroots level and the removal of obstacles to the greater good of humanity.

Synthesis of Ln-Srxmoyoz Nanoparticles and Their Application in Photocatalysis

In this work mixed metal oxides nanoparticles were synthesized containing “Mo” and “Sr” as basic elements and lanthanides (La & Gd) were doped using sonication, sol-gel and hydrothermal methods with variation in calcination temperature and reaction time. The nanomaterials synthesized were computed theoretically and later on compared photocatalytically. MoO3 nanoparticles were synthesized using sonication and sol-gel methods for 04 hours and calcined at 03 different temperatures 250, 350 and 450 °C. To conclude the best suitable method for the synthesis of MoO3 nanoparticles were characterized using fourier transform infra-red (FTIR), thermogravimetric analysis-diffraction scanning calorimetry (TGA-DSC), scanning electron microscopy-energy dispersive X-ray (SEM-EDX) spectroscopy, high resolution transmission electron microscopy (HRTEM), dynamic laser scattering-particle size analyser (DLS-PSA), X-ray diffraction (XRD) analysis and UV-Visible spectrometer. The optical properties like band gap, extinction coefficient (K), refractive index (n), optical conductivity (ρ), dielectric functions (εr and εi) and Urbach energy (EU) were determined. The sol-gel method were concluded the better one and later on used for the synthesis of MoO3 nanoparticles with the reaction time of 10 and 24 hours. SrMoO4 nanocomposites were synthesized by varying the “Sr” and “Mo” concentration with change in reaction time of 04, 10 and 24 hours using the sol-gel method. The nanocomposites were characterized using FTIR, Raman analysis, SEM-EDX, HRTEM, DLS-PSA, XRD and UV-Visible spectrometer. The refinement parameters were calculated with the help of XRDdata using FULLPROFF and PROFEX software. The optical properties like band gap, extinction coefficient (K), refractive index (n), optical conductivity (ρ), dielectric functions (εr and εi) and Urbach energy (EU) were determined. Lanthanides (La and Gd) doped SrMoO4 nanocomposites were synthesized using hydrothermal method and characterized using FTIR, Raman analysis, SEM-EDX spectroscopy, TEM, DLS-PSA, XRD analysis and UV-Visible spectrometer. The refinement parameters were calculated with the help of XRD-data using FULLPROF and PROFEX software. The optical properties like band gap, extinction coefficient (K), refractive index (n), optical conductivity (ρ), dielectric functions (εr and εi) and Urbach energy (EU) were determined. All the synthesized nanomaterials were computed theoretically using SCM-ADF/BAND and VESTA software using Density Function Theory (DFT) principles with Kohn-Sham approach. Different parameters like change in basis set, Hubbard potential, XC-functional (LDA, GGA, Meta and Model) were run to obtain the results closet to the experimental one. Relationship between theoretical and experimental band gap was observed. Density of state (DOS) analysis was performed and contribution of elements “Mo”, “O”, “Sr”, “Gd” and “La” were observed with respect to fermi energy. MOPAC software results in the geometry and frequency optimization using semi-empirical Hamiltonians calculations with PM7 code. VESTA software gives the complete 3D structural representation of synthesized nanoparticles and nanocomposites with the detailed lattice and structural parameters. The photo-catalytic activity of all the nanoparticles and nanocomposites were done against anthropogenic organo-pollutants 2-methyl-4-nitrophenol and 2-methyl-4,6dinitrophenol. These both organo-pollutants are used in military and textile industries. The results of photocatalysis are in relation to type of metal oxide, synthesis method, synthesis conditions, change in particle size and band gap are compared with respect to percentage degradation and kvalues.