Symmetries, Differential Equations and Applications

1. Front Matter

   Pages i-viii

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2. Normal Forms for Submanifolds Under Group Actions

   • Peter J. Olver

   Pages 1-25

3. Integrable Nonlocal Reductions

   • Metin Gürses, Aslı Pekcan

   Pages 27-52

4. Construction of Solvable Structures from \(\mathfrak {so}(3,\mathbb {C})\)

   • A. Ruiz, C. Muriel

   Pages 53-65

5. Classification of Scalar Fourth Order Ordinary Differential Equations Linearizable via Generalized Lie–Bäcklund Transformations

   • Hina M. Dutt, Asghar Qadir

   Pages 67-74

6. On the Symmetries of a Liénard Type Nonlinear Oscillator Equation

   • R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan

   Pages 75-103

7. Symmetries of Equations with Nonlocal Terms

   • Sergey V. Meleshko

   Pages 105-124

8. A Note on the Multiplier Approach for Derivation of Conservation Laws for Partial Differential Equations in the Complex Domain

   • R. Naz, F. M. Mahomed

   Pages 125-136

9. The Calculation and Use of Generalized Symmetries for Second-Order Ordinary Differential Equations

   • C. Muriel, J. L. Romero, A. Ruiz

   Pages 137-158

10. Differential Invariants for Two and Three Dimensional Linear Parabolic Equations

    • Adnan Aslam, Asghar Qadir, Muhammad Safdar

    Pages 159-177

11. Kaleidoscope of Classical Vortex Images and Quantum Coherent States

    • Oktay K. Pashaev, Aygül Koçak

    Pages 179-199

Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods.

The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory andapplications of Lie symmetry groups.

This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.

• Lie groups
• differential equations
• mathematical physics
• applied mathematics
• transformation methods
• applied mechanics
• physics
• ordinary differential equations

• Department of Mathematics, Massachusetts Institute of Technology, Department of Mathematics, Cambridge, USA

  Victor G. Kac

• School of Mathematics, University of Minnesota, Minneapolis, USA

  Peter J. Olver

• Department of Mathematics and Statistics, Université de Montréal, Montréal, Canada

  Pavel Winternitz

• Civil Engineering Dept, Div.of Mechanics, Istanbul Technical University, Civil Engineering Department, Div.of Mechanics, Maslak (Istanbul), Turkey

  Teoman Özer

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