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Chapter 1 Traveling Wave Solutions for the Diffusive Lotka-Volterra Equations with Boundary Problems 1.1 Introduction 1.2 Analysis of the method 1.3 Traveling wave solutions for Lotka-Volterra diffusion equations with boundary conditions 1.4 Numerical simulations Chapter 2 Dynamical Behavior and Traveling Wave Solutions in Optical Fibers with Schrodinger-Hirota Equation 2.1 Introduction 2.2 Bifurcation analysis and traveling wave solutions for the SHE 2.3 Traveling wave solutions via the complete discriminant system method Chapter 3 The Classification of Single Traveling Wave Solutions for the Fractional Coupled Nonlinear Schrodinger Equation 3.1 Introduction 3.2 An overview of the conformable derivative 3.3 Analysis of the method 3.4 Traveling wave solutions for the FCNLSE Chapter 4 Bifurcation Analysis and Multiple Solitons in Birefringent Fibers with Coupled Schrodinger-Hirota Equation 4.1 Introduction ¡­¡­