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 ltiple Solitons in Birefringent Fibers with Coupled Schrodinger-Hirota Equation 4.1 Introduction 4.2 Bifurcation analysis and multiple solitons for the CNLSHE 4.3 Some other dispersive optical solitons in birefringent fibers for the CNLSHE Chapter 5 Bifurcation Analysis and Optical Solitons for the Concatenation Model 5.1 Introduction 5.2 Optical solitons and phase portraits 5.3 Other optical solitons and classification References