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Darboux Transformation and Discrete Integrable Systems: Approach to Soliton Solutions

Thesis Info

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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

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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.
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اللغة العربية

اللغة العربية

(حسب ترتيب حروف الهجاء)

 

سنة الطبع

 

إسم المطبعه

 

إسم الكتاب

 

إسم المؤلف

الرقم

ط (2) 1401 هـ

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