1 The Research Process for Rogue Wave
1.1 The Research Process for Rogue Wave Phenomenon
1.2 Some Famous Experiments of Rogue Wave
1.3 Research Method and Physical Mechanism of Rogue Wave
1.3.1 Methodology of Rogue Wave
1.3.2 Physical Mechanism of Rogue Wave
1.4 Mechanisms of Rogue Wave
1.4.1 Linear Mechanisms of Rogue Wave
1.4.2 Nonlinear Mechanisms of Rogue Wave
1.5 Rogue Wave Solutions for Nonlinear Partial Differential Equations
1.6 Optical Rogue Wave
1.7 Financial Rogue Wave
1.8 Nonautonomous Rogue Wave Solutions
2 Construction of Rogue Wave Solution by the Generalized Darboux Transformation
2.1 The Classical Darboux Transformation
2.2 Generalized Darboux Transformation for the Classical KdV Equation
2.3 Darboux Transformation for N-Coupled Focusing NLS Equation
2.4 Rogue Wave Solutions for the Two-Component NLS Equation
2.4.1 Rogue Wave Solutions for the Two-Component NLS Equation
2.4.2 Bright-Dark-Breather and Rogue Wave
2.5 Generalized Darboux Transformation for NLS Equation
2.5.1 Generalized Darboux Transformation
2.5.2 Higher-Order Rogue Wave in Determinant Forms
2.5.3 Mathematical Characters of the Rogue Wave Solutions for Standard NLS Equations
2.6 Generalized Darboux Transformation for DNLS Equation
2.6.1 Darboux Transformation-I
2.6.2 Darboux Transformation-II
2.6.3 Reductions
2.6.4 Generalized Darboux Transformations
2.6.5 Generalized Darboux Transformations-II
2.6.6 High-Order Solutions for DNLS Equation
3 Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse scattering Method
3.1 Hirota Bilinear Method
3.1.1 Rogue Wave Solution for the NLS Equation
3.1.2 Rogue Wave Solution for the DS-I Equation
3.2 Reduction from the KP Equation
3.3 Algebro-Geometric Reduction Approach
3.3.1 Relationship between Fredholm Determinant and 0-Function
3.3.2 Relations between Fredholm and Wronskian Determinants
3.3.3 Construction of Rogue Wave Solution
3.4 Inverse Scattering Method and Rogue Wave
3.4.1 Direct Problem
3.4.2 Scattering Matrix
3.4.3 Involution Relation
3.4.4 Jumps of the Eigenfunctions and Scattering Data Across the Branch Cut
3.4.5 Time Evolution
3.4.6 Inverse Problem
3.4.7 Darboux Transformation and Rogue Wave Solutions
4 The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model
4.1 Introduction to the Rogue Wave Solution
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