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Modified G /G -Expansion Methods for Soliton Solutions of Nonlinear Differential Equations

Thesis Info

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External Link

Author

Shakeel, Muhammad

Program

PhD

Institute

HITEC University

City

Taxila

Province

Punjab

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/6666/1/Muhammad_Shakeel_Maths_2015_HITECTaxila.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726664010

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Solitons play a pivotal role in many scientific and engineering phenomena. Solitons are a special kind of nonlinear waves that are able to maintain their shape along the promulgation. From the last four decades, the rampant part of fundamental phenomenon of soliton has successfully attracted the researchers from the physical and mathematical sciences. Various branches of science like solid-state physics, plasma physics, particle physics, biological systems, Bose-Einstein-condensation and nonlinear optics are enjoying the benefits taken from soliton. Soliton research gives way to theoretical aspects such as soliton existence, computation of soliton profiles and soliton stability theory by using the tools of soliton dynamics and soliton interactions to applicative aspects. The hub of this thesis is to search not only for the solitary solutions of nonlinear differential equations but also for nonlinear fractional differential equations. This piece of writing targets to give an intuitive grasp for; Further Improved (G¢ /G) -expansion, Extended Tanh-function, Improved (G¢ /G) -expansion, Alternative (G¢ /G) -expansion with generalized Riccati equation, (G¢ /G, 1/G) -expansion and Novel (G¢ /G) - expansion methods. Moreover, we shall extend Novel (G¢ / G) -expansion method to nonlinear fractional partial differential equations arising in mathematical physics. For multifarious applications, all the methods are glib to follow. In addition, these methods give birth to several types of the solutions like hyperbolic function solutions, trigonometric function solutions and rational solutions. The premeditated methods are very efficient, reliable and accurate in handling a huge number of nonlinear differential equations.
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مولانا شریف الحسن

مولانا شریف الحسن
اس مہینہ کی پانچ تاریخ کی شام کوحضرت مہتم صاحب دارالعلوم دیوبند کے ٹیلی گرام سے اچانک یہ اطلاع ملی کہ دارالعلوم کے شیخ الحدیث مولانا شریف الحسن صاحب کا شب گزشتہ یکایک انتقال ہوگیاتو جی دھک سے ہوکررہ گیا اور دل ودماغ پرایک سلسلہ حزن والم کی کیفیت طاری ہوگئی۔ مولانا کی عمر ستر کے لگ بھگ ہوگی، اس کے باوجود اپنے فرائض منصبی کی انجام دہی میں نہایت چست اورمستعد تھے۔ چند برسوں سے مختلف اسقام وعوارض میں مبتلا تھے آخر میں ان کو دل کاروگ بھی لگ گیا تھا اورغالباً یہی ان کی مرگ مفاجات کاسبب ہوا۔اناﷲ واناالیہ راجعون۔
مولانا علم وعمل، تقوی وطہارت اورفضائل وشمائل ہراعتبار سے اکابر دیوبند کی یادگار اوران کا نمونہ تھے۔ تمام علوم وفنون میں استعداد نہایت پختہ تھی مگر حدیث سے ان کو طبعی طورپر بڑا شغف اور لگاؤ تھا۔برسوں جامعۂ اسلامیہ ڈابہیل میں صحیح بخاری کادرس بڑی شان اورآن بان سے دیتے رہے، جب دارالعلوم دیوبند کو ان کی ضرورت ہوئی تواس کی طلب پر یہاں چلے آئے، یہاں انہوں نے ایک نہایت نازک موقع پر دارالعلوم کی ایسی شاندار خدمت انجام دی کہ دارالعلوم ایک عظیم فتنہ اورابتلا سے بچ گیا۔ سابق شیخ الحدیث مولانا فخر الدین صاحب کے انتقال کے بعد بخاری جلداوّل کے درس کاکوئی معقول اورخاطر خواہ انتظام ارباب بست وکشاد کی سمجھ میں نہیں آرہا تھا، کیونکہ اگرچہ دارالعلوم میں خدا کے فضل وکرم سے حدیث کے بڑے اچھے اچھے استاد اورمدرس ہیں لیکن بخاری جلد اوّل کامعاملہ دوسری کتب حدیث سے بالکل الگ اورمختلف ہے، یہ ایک کتاب یاایک فن نہیں بلکہ دسیوں علوم وفنون کے دقیق مباحث کا مجموعہ ہے۔ دارالعلوم دیوبند کاسب سے بڑا امتیاز ہی درس بخاری ہے۔اس بنا پر یہاں اس مسند پروہی عالم بیٹھ سکتاہے جس کوسالہاسال بخاری کے درس اوراس کے...

POLA PEMBINAAN KEAGAMAAN PESERTA DIDIK MELALUI PROGRAM PALU KANA MAPANDE (PKM) DI KOTA PALU

This study discusses the pattern of religious guidance of learners through PKM program, learning interests, and the implications of religious guidance through PKM program in Elementary School Inpres Perumnas Palu Barat. This research is a qualitative descriptive research based on phenomenological approach, that is describing various events and its relation to learners in certain situations. Data collection is done through observation, interview, and documentation. The results showed that the pattern of religious guidance through PKM program in SDN Gugus IV (SD Inpres Perumnas) was greeted enthusiastically by the students. However, the interest of learners in following religious coaching is different, some are very enthusiastic, but some of them not enthusiastic. The implication of religious guidance through PKM program can correct and improve the ability of learners in reading and writing verses of Al Quran. They can also actualize memorization materials, daily prayers, and understand the procedures of worship in daily life.

Genetic Analysis of Autosomal Recessive Intellectual Disability in Consanguineous Families

Intellectual disability (ID) is a common and highly heterogeneous neurodevelopmental disorder. It affects 1–3% of the world’s population and its prevalence is almost twice as high in underdeveloped than in affluent world. ID has an enormous socio-economic burden and devastating impact on the lives of affected individuals and their families. More than 700 genes have been discovered so far across different studies pertaining to X-linked, autosomal dominant and recessive ID. Autosomal recessive intellectual disability (ARID), being the most common form of ID. Till date, more than 577 genes involved in ARID have been discovered mostly in consanguineous communities. ARID is further grouped into syndromic ARID (nARID) and non-syndromic ARID (nsARID) types primarily based upon the phenotypic appearance. In Pakistan, the rate of consanguinity is approaching 70% and this high rate results in higher rates of recessive disorders including ARID. Inbred families provide a unique opportunity to find pathogenic variants in known as well as candidate genes responsible for recessive disorders due to the extensive regions of homozygosity in the genomes of these individuals. We enrolled 25 suspected consanguineous ARID families based on pedigree analysis and clinical evaluation from Kohat district, KPK province of Pakistan. The identified consanguineous families were subjected to genetic analysis through Whole exome sequencing (WES) and genome-wide SNP array. Bioinformatics analysis was carried out using Genome Analysis Tool Kit (GATK) based bioinformatics pipeline and Consanguinity Analysis Through Common Homozygosity (CATCH) software. Subsequent prioritization was carried out by application of various quality filters. Finally, the selected putative causative variants were validated by Sanger sequencing. Out of 25 families, known causative mutations in five known genes (ASPM, ATRX, GPR56, NAGLU and DOLK) were identified in eight different families for ARID. Furthermore, novel mutations in seven known ID genes (ABAT, SLC12A6, SHANK3, BCKDK, DDHD2, ERCC2 and GPT2) were found in seven families. Three potential likely pathogenic mutations were identified in three different families in three novel genes (DYNC1I2, FBXL3 and LINGO1). However, seven families remained unsolved; probably we missed the causative variants. Our study showed that v exome sequencing in combination with microarray genotyping is a powerful technique to find out the causative variants in rare ARID families and can be used to establish correlation between candidate genes and phenotypes. The diagnostic yield of the strategy used in our whole ID project was found to be approximately 32% (32/100). Furthermore, the present work also revealed that the genetic variations are associated with a significant number of consanguineous ARID families from Pakistan.