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Chapter 1 Traveling Wave Equations of Some PhysicalModels1 The model of nonlinear oscillations of hyperelastic rods2 Higher order wave equations of Korteweg-De Vries type3 Camassa-Holm equation and its generalization forms4 More classes of equations of mathematical physicsChapter 2 Basic Mathematical Theory of the Singular Traveling Wave Systems2.1 Some preliminary knowledge of dynamical systems2.2 Phase portraits of traveling wave equations having singular straight lines.2.3 Main theorems to identify the profiles of waves and some examplesChapter 3 Bifurcations of Traveling Wave Solutions of Nonlinear Elastic Rod Systems3.1 Bifurcations of phase portraits of (3.0.1) and physical acceptable solutions3.2 Four types of solitary waves and three types of periodic waves3.3 The non-periodic behavior of axial motionsChapter 4 Bifurcations of Traveling Wave Solutions of Generalized Camassa-Holm Equation4.1 Bifurcations of phase portraits of system (4.0.2)4.2 Exact parametric representations of traveling wave solutions of (4.0.1)4.3 The existence of smooth solitary wave solutions and periodic wave solutionsChapter 5 Bifurcations of Traveling Wave Solutions of Higher Order Korteweg-De Vries Equations5.1 Traveling wave solutions of the second order Korteweg-De Vries equation in the parameter condition group (I)5.2 Traveling wave solutions of the second order Korteweg-De Vries equation in the parameter condition group (II)5.3 Traveling wave solutions for the generalization form of modified Korteweg-De Vries equationChapter 6 The Bifurcations of the Traveling Wave Solutions of K(m, n) Equation6.1 Bifurcations of phase portraits of system (6.0.2)6.2 Some exact explicit parametric representations of traveling wave solutions6.3 Existence of smooth and non-smooth solitary wave and periodic wave solutions6.4 The existence of uncountably infinite many breaking wave solutions and convergence of smooth and non-smooth traveling wave solutions as parameters are variedChapter 7 Kink Wave Solution Determined by a Parabola Solution of Planar Dynamical Systems7.1 Six classes of nonlinear wave equations7.2 Existence of parabola solutions and their parametric representations7.3 Kink wave solutions of 6 classes of nonlinear wave equationsChapter 8 Traveling Wave Solutions of Coupled Nonlinear Wave Equations8.1 Traveling wave equation of the Kupershmidt's equation8.2 Bifurcations of phase portraits of (8.¡¡7)8.3 Existence of smooth solitary wave, kink wave and periodic wave solutions8.4 Non-smooth periodic waves and uncountably infinite many breaking wave solutionsChapter 9 Solitary Waves and Chaotic Behavior for a Class of Coupled Field Equations9.1 Solitary wave solutions of the integrable case of (9.0.1)9.2 The existence of small amplitude periodic solutions9.3 Chaotic behavior of solutions of (9.0.2)9.4 The existence of arbitrarily many distinct periodic orbitsChapter 10 Bifurcations of Breather Solutions of Some Nonlinear Wave Equations10.1 Introduction10.2 Bifurcations of traveling wave solutions of system (10.7) when VRP (¦È, r) given by (10.2)10.3 Traveling wave solutions of system (10.1) with VRP (¦È, r) givenby (10.2)10.4 Bifurcations of solutions of (10.7) with VRP (¦È, r) given by (10.3)10.5 Traveling wave solutions of (10.1) with VRP (¦È, r) given by (10.3)10.6 Bifurcations of breather solutions of (10.4)Chapter 11 Bounded Solutions of (n+1)-Dimensional Sineand Sinh-Gordon Equations11 (n+1)-dimensional Sine-and Sinh-Gordon equations12 The bounded solutions of the systems (14) and (15)13 The bounded traveling wave solutions of the form (12a) of(11)Chapter 12 Exact Explicit Traveling Wave Solutions for Two Classes of (n+1)-Dimensional Nonlinear Wave Equations12.1 (n+1)-dimensional Klein-Gordon-Schrodinger equations12.2 (n+1)-dimensional Klein-Gordon-Zakharov equationsReferences