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Intro; Preface; Contents; Normal Forms for Submanifolds Under Group Actions; 1 Introduction; 2 Plane Curves; 3 Normal Forms for Submanifolds; References; Integrable Nonlocal Reductions; 1 Introduction; 2 AKNS System; 3 Standard and Nonlocal NLS Equations; 4 Standard and Nonlocal MKdV Equations; 5 Fordy-Kulish System; 6 Nonlocal Fordy-Kulish Equations; 7 Super Integrable Systems; 8 Nonlocal Super NLS and MKdV Equations; 8.1 Super NLS Equations; 8.2 Super MKdV Systems; 9 Concluding Remarks; References; Construction of Solvable Structures from mathfrakso(3,mathbbC); 1 Introduction
2 Solvable Structures for ODEs3 Solvable Structures from mathfrakso(3,mathbbC) for Third-Order ODEs; 4 First Integrals and Parametric General Solution; 5 Examples; 5.1 Example I; 5.2 Example II; 6 Concluding Remarks; References; Classification of Scalar Fourth Order Ordinary Differential Equations Linearizable via Generalized Lie-Bäcklund Transformations; 1 Introduction; 2 Generalized Lie-Bäcklund Transformations; 2.1 Group Classification; 3 Conclusion; References; On the Symmetries of a Liénard Type Nonlinear Oscillator Equation; 1 Introduction; 2 Lie Point Symmetries of Eq.(1)
3 Methods for Solving Determining Equations3.1 Expanding Coefficients of an Admitted Generator in Taylor Series; 3.2 Using Arbitrariness of Integral Terms; 3.3 A Method of Preliminary Group Classification; 4 Symmetries of Integro-Differential Equations; 4.1 The Boltzmann Equation and Its Models; 4.2 Population Balance Equations; 4.3 Viscoelastic Materials with Memory; 4.4 Evolutionary Integro-Differential Equations Describing Nonlinear Waves; 4.5 Kinetic Equation in a Nonlinear Thermal Transport Problem; 5 Symmetries of Delay Differential Equations; 5.1 Nonlinear Klein-Gordon Equation
5.2 Delay Ordinary Differential Equations6 Applications to Stochastic Differential Equations; 6.1 Symmetries of Stochastic Fluid Dynamics Equations; 6.2 Trajectory Approach; 6.3 Linearization of Systems of Two Second-Order Equations; References; A Note on the Multiplier Approach for Derivation of Conservation Laws for Partial Differential Equations in the Complex Domain; 1 Introduction; 2 The Multiplier Approach: Complex and Real Domains; 3 Applications; 3.1 The Nonlinear Spherical KdV Equation in the Complex Domain; 3.2 The Complex Maxwellian Tails Equation
2 Solvable Structures for ODEs3 Solvable Structures from mathfrakso(3,mathbbC) for Third-Order ODEs; 4 First Integrals and Parametric General Solution; 5 Examples; 5.1 Example I; 5.2 Example II; 6 Concluding Remarks; References; Classification of Scalar Fourth Order Ordinary Differential Equations Linearizable via Generalized Lie-Bäcklund Transformations; 1 Introduction; 2 Generalized Lie-Bäcklund Transformations; 2.1 Group Classification; 3 Conclusion; References; On the Symmetries of a Liénard Type Nonlinear Oscillator Equation; 1 Introduction; 2 Lie Point Symmetries of Eq.(1)
3 Methods for Solving Determining Equations3.1 Expanding Coefficients of an Admitted Generator in Taylor Series; 3.2 Using Arbitrariness of Integral Terms; 3.3 A Method of Preliminary Group Classification; 4 Symmetries of Integro-Differential Equations; 4.1 The Boltzmann Equation and Its Models; 4.2 Population Balance Equations; 4.3 Viscoelastic Materials with Memory; 4.4 Evolutionary Integro-Differential Equations Describing Nonlinear Waves; 4.5 Kinetic Equation in a Nonlinear Thermal Transport Problem; 5 Symmetries of Delay Differential Equations; 5.1 Nonlinear Klein-Gordon Equation
5.2 Delay Ordinary Differential Equations6 Applications to Stochastic Differential Equations; 6.1 Symmetries of Stochastic Fluid Dynamics Equations; 6.2 Trajectory Approach; 6.3 Linearization of Systems of Two Second-Order Equations; References; A Note on the Multiplier Approach for Derivation of Conservation Laws for Partial Differential Equations in the Complex Domain; 1 Introduction; 2 The Multiplier Approach: Complex and Real Domains; 3 Applications; 3.1 The Nonlinear Spherical KdV Equation in the Complex Domain; 3.2 The Complex Maxwellian Tails Equation